A year after the success of the city’s 2012 Olympic bid, the Prime Minister said that it would be fitting to field a British team for the first time in 56 years. “You have to get all the federations to agree,” Mr Blair said. “I think it would be a good idea. When you are hosting the Olympics and you have lots of countries who send their teams, it would be a shame if we didn’t have one of our own.”

Of the four British football federations, England and Northern Ireland have given their backing to a united team, but Wales and Scotland have not.

Mr Blair described the intensive lobbying that took place in Singapore to secure the Games. But he admitted that he had not believed Britain could win, and, on one occasion, confusing athletes after his briefing cards became mixed up. “The really odd thing was that I went to Singapore really not believing that we would win. I thought maybe we had a good chance, but I kind of believed a lot of the pre-publicity that it was unlikely that anyone other than Paris would win it.”

During meetings with the International Olympic Committee members Mr Blair was handed cards with information about each of his guests before their arrival. However, on one occasion he found himself uncertain of who he was talking to. “It was an ice- skater who turned out to be a javelin-thrower,” he said. “Or the other way round. At one point the cards were getting mixed up, the wrong CVs were coming in. I was thinking ‘this guy doesn’t look like a javelin-thrower’. He then said to me, ‘My main concern is about the quality of the ice’. And I thought ‘work that one out, javelin-throwing must have really changed’.

Someone behind him was making frantic gestures that suggested he wasn’t a javelin-thrower after all.”

London’s victory came with a pledge by Lord Coe, the bid chairman, that the London Games would bring participation and interest in Olympic sport back to young people. A year later, there has been limited evidence of this, although Mr Blair said he hoped that this would change.

“When I was at school, you could play sport every day and many of us did,” he said. “It was a great thing to be able to do. I’d like the opportunity for kids to be able to play sport.”

In the two most recent Olympics, half of Team GB’s medal winners have been athletes educated at private schools. Mr Blair said that he hoped that British medal winners could be more representative, “but it requires us to build the facilities and encourage sport in schools. I think sport is a major, major thing. It declined over a long period of time and we’ve got to build it back up again.”

Examples of the reconstruction process, he said, included “the huge investment going into school-building and school sport in the next few years”.

The Government has set a target of four hours of sport a week for children by 2010. Another target, about which Mr Blair is less concerned, is reaching fourth place in the Olympic medal table — a goal set by the British Olympic Association.

“It would be good if we could do it,” he said. “You want to get as many medals as you can, but at the end the most important thing is the legacy of regeneration in this part of London, which will be immense for hundreds and thousands of people.”