They said US and Taliban representatives will hold bilateral meetings, with Afghan President Hamid Karzai’s High Peace Council expected to follow up with its own talks a few days later.

One US official said: “I think the US will have its first formal meeting with the Taliban, and the first meeting with the Taliban for several years, in a couple of days in Doha.

“I would expect that to be followed up within days by a meeting between the Taliban and the High Peace Council, which is the structure that President Karzai has set up for talks of this nature.”

Taliban representative Mohammed Naeem told a news conference the group wanted good relations with its neighbours.

He said: “We want to keep good relations with all of the world countries, in particular with our neighbouring countries.

“But the Islamic emirate (Taliban) sees the independence of the nation from the current occupation as a national and religious obligation.”

A Taliban statement added: “We support a political and peaceful solution that ends Afghanistan’s occupation, and guarantees the Islamic system and nationwide security.”

No date has been set for any talks.

The Taliban opened its Doha office on Tuesday and plans to hold talks with Mr Karzai’s government on ending the conflict which erupted after US troops ousted them from power in 2001 after the September 11 attacks.

The process is likely to take some time. The US will insist the Taliban breaks all ties with al Qaeda, end violence and accept the Afghan constitution.

It comes hours after Afghan government forces formally took over responsibility for national security from a NATO combat mission scheduled to leave the country next year.

The security handover at a military academy outside Kabul marked a major milestone in the US-led combat mission.

It includes the last 95 districts with areas in the south and east where the Taliban has concentrated its insurgency since 2001.

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But it does not look to be a completely dry day.

The heat will trigger some heavy showers and thunderstorms across southern England and East Anglia, lasting into the night.

Weather experts say this wet end is not unusual.

Sky News Weather Presenter Nazaneen Ghaffar said: “This pattern of weather is not unusual at this time of year.

“In fact, it is well summarised by the well-known, if somewhat tongue in cheek, definition of a British summer – three fine days then a thunderstorm.”

For those further north and in the west of the UK and in Ireland it will remain drier but not as hot.

On Thursday, temperatures will fall back to the low 20Cs.

The welcome warm blast follows what the Met Office said was the coldest spring since 1962.

There was a mean temperature across March, April and May of 6C (43F), which is calculated as being 1.7C below the long-term average.

:: Proud of your photo skills? Upload your pictures to the glorious summer section on Sky’s Your Photos.

She said she repeatedly asked doctors at Leicester Royal Infirmary for a scan but was told she did not need it.

Her initial treatment at the LRI was good, but then there were further complications.

She told Gem: “After I finished treatment in August 2011, I started getting pains in my left shoulder and the back of my head.  I had breast cancer on my left, so I wondered whether it was related.”

She also approached Glenfield Hospital, which told her a scan was not needed.

Last month, when the pain was unbearable, Mrs Scrimshire had a scan which showed four large tumours in her brain.  She has been given just weeks to live.

Her husband Mark, is now considering suing Leicester Hospital’s NHS Trust.  He believes the real reason his wife wasn’t offered a scan was because of money.

“She should have been a priority, after being diagnosed with breast cancer, she should have been listened to and scanned, just for peace of mind.  They’re telling me patients aren’t scanned after treatment, because of national guidelines, but I’m saying let’s change that, let’s make it happen that Lindsey’s legacy that every cancer patient gets scanned.”

In a statement Leicester Hospital’s NHS Trust said:

“We are sorry that Lindsey did not receive a scan at her follow up appointment but it was felt at the time the symptoms were not related to the breast cancer.

“Our thoughts are with Lindsey and her family during this time and we have met with them to discuss the treatment options.

“Lindsay’s treatment for breast cancer back in 2011 was completely appropriate and under national guidance we do not scan patients after treatment. We are happy to meet again to discuss any of their concerns.”

The pair were pictured having an argument on the terrace of a restaurant on June 9.

Lawson, 53, the daughter of former chancellor Lord Lawson, was reportedly seen weeping following the episode outside Scott’s in Mayfair, central London.

Speaking to the London Evening Standard on Monday, Saatchi said: “About a week ago, we were sitting outside a restaurant having an intense debate about the children, and I held Nigella’s neck repeatedly while attempting to emphasise my point.

“There was no grip, it was a playful tiff.

“The pictures are horrific but give a far more drastic and violent impression of what took place.

“Nigella’s tears were because we both hate arguing, not because she had been hurt.

“We had made up by the time we were home. The paparazzi were congregated outside our house after the story broke yesterday morning, so I told Nigella to take the kids off till the dust settled.”

Lawson’s spokesperson has said that there would not be any comment on Saatchi’s explanation but did confirm that she “isn’t at the family home”.

Police confirmed that they had not received a complaint of assault from Lawson or anyone else.

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They will be expected to come up with ways to stop access to child abuse images and report back with an action plan.

The meeting comes after two child killers were found to have viewed child pornography online.

Mark Bridger, convicted of murdering five-year-old April Jones, and Stuart Hazell, who murdered Tia Sharp, 12, both accessed abusive images.

In the 12 days since the summit was announced, web giants have already taken some action.

TalkTalk and BT have announced that customers trying to view inappropriate material will be confronted by a pop-up warning.

And Google has pledged millions of pounds to organisations who try and tackle child abuse online, such as the Internet Watch Foundation who maintain a blacklist of images.

Culture Secretary, Maria Miller said:  “Child abuse images are horrific and widespread public concern has made it clear that the industry must take action. Enough is enough.

“In recent days we have seen these companies rush to do more because of the pressure of an impending summit. Imagine how much more can be done if they seriously turn their minds to tackling the issue. Pressure will be unrelenting.”

It is unclear exactly what concrete action – if any – the government will demand from the meeting.

Companies providing internet services in Britain have already rejected a call from the Prime Minister’s adviser to impose parental filters for adult content as a default setting when viewing content online.

The Internet Service Providers Association said it remained opposed to default filtering because it “can be circumvented and lead to over- or under-blocking” of offensive web pages.

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The Ministry of Defence (MoD) said the move was necessary to help balance the books but insisted operational capability would not be affected.

Defence Secretary Philip Hammond has confirmed there will be no further reductions in manpower in the next round of spending cuts.

But shadow defence secretary Jim Murphy said the redundancy notices being issued today “represent not just broken promises but a failing strategy” to reform the British Army.

The MoD said it had attempted to maximise the number of voluntary redundancies.

A spokeswoman said: “Tough decisions needed to be made to address the multi-billion pound deficit and bring the defence budget back into balance.

“This unfortunately included making some redundancies across the armed forces. However we can be clear that these reductions will not affect our operational capability.

“The end of combat operations in Afghanistan and the restructuring of our armed forces means they will be more reflective of the complex global situation and more adaptable to future challenges and threats.”

But Mr Murphy said: “The Government has a flawed plan for reforming the British Army. There is a huge effort going into sacking soldiers but nowhere near as much is being done to plug the gap by recruiting new reservists.

“These redundancies represent not just broken promises but a failing strategy, and the level of voluntary applicants will be a signal of morale.”

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The former England and Manchester United star will travel to four Chinese cities - Hangzhou, Beijing, Shanghai and Nanjing –  and visit several Chinese Super League clubs.

On his first trip to the country in an official role with the league since his retirement from Paris Saint-Germain, Beckham has donated several football shirts to help raise funds for children’s charities.

Beckham’s visit comes at a poor time for Chinese football –  the national squad has lost all three of their recent friendlies, including a defeat relative minnows Thailand on Saturday.

The attacks spanned three decades and involved children aged as young as nine.

A “small number” of complaints have been made about the sentence, prompting an investigation by the Attorney General’s Office which has the power to refer the sentence to the Court of Appeal.

A lawyer representing some of Hall’s victims said they felt “vindicated” after the sentencing.

Harrowing details of the sex abuse suffered by his victims were described at Preston Crown Court.

The prosecution told how a 13-year-old victim was assaulted after they had played tennis, when he is said to have told her: “Sometimes thank you was not enough in words.”

He told a 10-year-old girl to cuddle him “like she would one of her teddies” after he had given her steak and champagne, the court heard.

A 15-year-old girl was abused in Hall’s dressing room at the BBC, prosecutors said.

A 13-year-old was assaulted while she was drunk and unwell at a family party and described the attack as a “frenzied maul”.

He preyed on a nine-year-old girl while she was in bed.

Another victim, who was 17 at the time, was attacked while dressed as a cheerleader for the filming of It’s A Knockout.

Hall was told by Judge Anthony Russell during sentencing that those who had admired him in his career now know there is a “darker side” to him.

He was given sentences ranging from three months to 15 months, all to run concurrently. Judge Russell said Hall would have received 20 months after a trial but he reduced the sentence to reflect his guilty pleas.

He said there was a degree of planning and premeditation in some of the assaults and he criticised Hall’s initial “brazen” attitude when charged.

The judge said: “Several of these cases reveal an abuse of power by you because your status gave you an influence and standing which you abused.”

He added: “The repeated sexual abuse of young children, too young to consent and in no position to resist your advances, even if the individual acts are relatively mild, is a serious crime and it must be made clear to anyone tempted to take advantage of young children and other vulnerable victims that they face condemnation and punishment.”

Hall was branded a child abuse “predator” by prosecutors.

He initially told police his victims were lying as part of a “vendetta” against people in the public eye.

When arrested last December over three claims of indecent assault, he described the allegations as “nonsense”.

He told an officer one of the complainants was “a complete and utter liar”.

Hall, of Wilmslow, Cheshire, went on to issue an impassioned on-camera denial of any wrongdoing, describing the allegations against him as “cruel”.

But he would later admit 14 indecent assaults on 13 girls between 1967 and 1987.

The initial publicity around his arrest led to other women coming forward, including a 22-year-old who said she had been raped by Hall in the 1970s.

The rape charge was denied by Hall and has been left on file.

Hall’s defence barrister Crispin Aylett told the court his offences were at the “less serious end of the scale”.

He said Hall’s life was “unblemished” in the years since the offences, and statements were submitted about Hall’s charity work.

Mr Aylett, explaining his client’s TV work, said he had “brought laughter to millions” and that if he were jailed, he might die in prison.

Mr Aylett criticised some media reports about the case since Hall pleaded guilty and asked the judge to carry out the sentencing with a degree of proportion.

He said his client had been arrested “as a consequence” of the investigations into Jimmy Savile, “who used young girls on a scale that is simply staggering”.

Hall – who also faces civil claims from some of his victims – showed no emotion as he was led from the dock to begin his sentence.

Alan Collins, from law firm Pannone, which is representing some of the victims who attended court today – said the sentence sent out “a strong and uncompromising message that abusers will not escape justice”.

Commenting on behalf of his clients, he added: “I have spoken to a number of them already and they all feel vindicated that their allegations of abuse have been proven by Hall’s admission of guilt.

“He had previously denied allegations and accused his victims of lying. This was hurtful, distressing and insulting for them.

“We should remember that the youngest of this man’s victims was just nine-years-old and a custodial sentence is no more than he deserves.”

Labour confirmed that Shadow Attorney General Emily Thornberry had written to Dominic Grieve urging him to refer the sentences to the Court of Appeal because “it is unduly lenient”.

Detective Superintendent Neil Esseen of Lancashire Police’s major investigation team praised the victims for coming forward to report the abuse.

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“You now live in a thoroughly modern Northern Ireland.”

His young audience has been described as “the generation of peace” – people born after the ceasefires.

He said day-to-day life was changing “throughout the north”, adding that there was a time when a gathering of world leaders in Northern Ireland would have been “unimaginable”.

The president and his wife Michelle were introduced by 16-year-old schoolgirl Hannah Nelson, who said she wanted to see a permanent peace in her homeland.

“We should not let the past pull us apart and stop us moving forward. Somehow we need to make a brighter future, a future that builds bridges and brings people together,” she said.

Mr Obama’s comments took on a particular significance with the G8 summit in Lough Erne looking set to be dominated by international tensions over Syria.

Earlier, David Cameron said he is “as worried as anyone” about terrorist and extremist elements among opposition forces fighting to oust President Bashar Assad, and no decision has been made on arming the Syrian opposition.

The ongoing conflict in Syria threatens to overshadow the summit’s scheduled discussions on trade, tax and transparency, after Mr Obama announced he was ready to start supplying weapons to the rebels seeking to overthrow Mr Assad.

Speaking at Lough Erne, Mr Cameron said: “Let’s be clear – I am as worried as anybody else about elements of the Syrian opposition, who are extremists, who support terrorism and who are a great danger to our world.

“The question is what do we do about it? My argument is that we shouldn’t accept that the only alternative to Assad is terrorism and violence.

“We should be on the side of Syrians who want a democratic and peaceful future for their country and one without the man who is currently using chemical weapons against them.

“What we can try and do here at the G8 is have further pressure for the peace conference and the transition that is needed to bring this conflict to an end.”

Mr Cameron and Russian President Vladimir Putin met in London on Sunday to discuss the crisis in Syria, but appeared to have reached little common ground.

At a joint news conference, Mr Cameron acknowledged there were “big differences” between the two leaders on who was to blame for the conflict but insisted they could be overcome.

Mr Putin strongly defended the supply of arms by Moscow to Mr Assad’s “legitimate” government, but also stressed he wanted to achieve a diplomatic solution to the crisis.

He said he believed the G8 summit  is “one of the most appropriate means” to seek an end to the conflict.

When Mr Putin was asked by British journalists about comments by Mr Cameron last year – that those supporting Mr Assad had the blood of Syrian children on their hands – he reacted angrily.

He said: “One does not need to support people who not only kill their enemies, but open up their bodies, eat their intestines in front of the public and cameras. Are these the people you want to support?

“Is it them you want to supply with weapons? Then this probably has little relation to humanitarian values that have been preached in Europe for hundreds of years.”

Mr Putin and Mr Obama will hold a separate bilateral meeting at the Lough Erne resort.

Mr Cameron is hosting both presidents and the political leaders of Canada, France, Germany, Italy and Japan at the plush golfing venue.

On Monday London mayor Boris Johnson publicly warned against arming the rebels, suggesting the weapons could end up in the hands of “al Qaeda-affiliated thugs”.

The summit is taking place amid a security operation of unprecedented scale, with some 8,000 police officers – 3,600 of them borrowed from forces in England, Scotland and Wales – on patrol.

Vehicle checkpoints are back on the streets, there is a no-fly-zone over the venue and an “armada” of security vessels is patrolling a secure stretch of Lough Erne.

Police have warned of significant disruption. Eight world leaders and their entourages will be on the move. Some 8,000 students sitting exams were advised to travel to school early.

With Mr Obama engaged in the serious business of world politics, the First Lady and their daughters will pay private visits to Dublin and Wicklow.

Two years ago, the president and his wife went to Moneygall in County Offaly, from where his great, great, great grandfather, Falmouth Kearney, emigrated in 1850 before settling in Indiana.

:: Watch Sky News’ live coverage of the G8 summit on satellite channel 501, Virgin Media channel 602, and Freeview channel 82.

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Lawson, 53, the daughter of former chancellor Lord Lawson, was reportedly seen weeping following the episode outside Scott’s in Mayfair, central London.

Speaking to the London Evening Standard, Saatchi said: “About a week ago, we were sitting outside a restaurant having an intense debate about the children, and I held Nigella’s neck repeatedly while attempting to emphasise my point.

“There was no grip, it was a playful tiff.

“The pictures are horrific but give a far more drastic and violent impression of what took place. Nigella’s tears were because we both hate arguing, not because she had been hurt.

“We had made up by the time we were home. The paparazzi were congregated outside our house after the story broke yesterday morning, so I told Nigella to take the kids off till the dust settled.”

Lawson’s spokesperson has been quoted as saying: “I can clarify that she has left the family home with her children.”

Scotland Yard said that officers from the Community Safety Unit are “carrying out preliminary inquiries” after the photographs appeared in the Sunday People newspaper.

A spokesman said: “Inquiries are in hand to establish the facts in order to assess whether an investigation is necessary.”

They added that initial inquiries are at a very early stage and they will not discuss who might be spoken to in relation to the claims made in the newspaper.

Police confirmed that they had not received a complaint of assault from Lawson or anyone else.

The Community Safety Unit is designed to tackle hate crime, and the types of incidents they investigate include domestic violence, homophobia and racism.

Both are said to be regular visitors to the upmarket restaurant in Mount Street, with one report claiming that the couple were there on Saturday, less than a week after the alleged row.

A spokesperson for Scott’s said: “The staff and management at Scott’s are aware of the reports in the media and would like to make it clear that they did not see the alleged incident nor were they alerted to it at the time.”

Lawson wed Saatchi, 70, who made his name in advertising, in 2003.

She has two children, Cosima and Bruno, from her marriage to journalist John Diamond, who died of throat cancer in 2001.

She became a household name in 1998 with her first cookery book, How To Eat.