Boris in the blue corner batting for London 2012

Ken Livingstone's successor is adamant that the 2012 Olympics must leave a lasting legacy for Britain, and that sport has a crucial role to play in society. Just don't watch him playing it

Boris Johnson makes a positive impression on the children at a primary schools swimming gala in Dulwich last week (Robert Hallam)

What Ken Livingstone knew about sport could be written on the back of an Oyster card. "I'm not a sporty mayor," he confessed during the run-up to London's successful 2012 Olympics bid. "I really couldn't care less about sport. The nearest I've been to it was a snooker table at college." While a lack of passion for sport was about the only thing he had in common with Lady Thatcher, he was apparently converted to its political worth on the road to Damascus – or rather, Stratford – conning the Government (his phrase) into splashing the taxpayers' cash via the Olympics into his expansive regeneration plans for east London.

Now that London's sporting colours have changed from Red Ken to Boris Blue, his successor becomes a key player in the Olympics game, clearly concerned that the inheritance of the Livingstone legacy is something he has to live with. But in his first interview on sport and the Olympics since he took office last month, Boris Johnson told The Independent on Sunday he will be tackling the soaring costs of the Games head-on, a not- unfamiliar approach judging from his tactics on the football field.

"We are looking at ways of saving," says Johnson. "Everybody is worriedwe are going to waste squillions on projects that are going to have no lasting benefit for east London. That is why I want to make sure that there is a proper legacy. I'll be using my position on the Olympic Board to make sure that we deliver value for money not only for London, but the whole country.

"We are going to see some action. We need a master plan and we must get our skates on. While we pour all this money into an Olympic stadium, aquatic centre, media centre and all the rest, we've got to think: 'What's it going to be in five years' time?' We don't want to sink billions into east London without a long-term benefit, and keeping a cap on the costs. Regeneration is wonderful but the Olympics are about sport."

Johnson's first move as mayor was the highly controversial appointment of the feisty ex-Labour sports minister Kate Hoey as London's sports mistress – her official title is Commissioner for Sport – and she will be his cardmarker too. There is no doubting his genuine regard for sport, yet Johnson barely knows anyone in the game. But, like Livingstone, he knows how to play it politically.

He has already left his footprint on sport without dipping a toe into the mainstream. He has turned up at several youth events, such as the primary schools swimming gala in Dulwich last week, when such was the ecstatic clamour on his arrival that you would have thought the 300 kids were greeting Becks, not Boris. "Standing in a clammy, overheated swimming pool, watching a kids' competition and feeling the adrenalin takes you back to the terror you experienced yourself," he said. "You remember diving in and fearing your trunks might be coming off. I once swam in a schools competition and was so slow my teacher told me never to do it again."

While clearly he is more at home on Have I Got News For You than A Question of Sport, he has been a bit of a player himself. "I once challenged Seb Coe to a race down Fifth Avenue in New York. Obviously I couldn't win. He's rather fast, you know. But I love any kind of physical exertion, it's made me what I am."

At Oxford he played rugby as a tighthead prop for his college, Balliol. He jogs and cycles regularly. His son Milo, 13, one of his four children, is captain of his school football team and a promising cricketer who is having trials with Surrey.

Johnson says: "I love sport but the fact is I'm no bloody good at it. Anyone who's seen that video clip of me attempting to play [in a charity match] will know that I am not God's gift to football, but I think it's incredibly important for building self-confidence, team work, competitive spirit, ability to cope with failure, all that stuff, which is so hard for kids these days.

"When I was running for mayor I was always conscious of the part sport might play in my life for the next four years. One of the things that made me really excited about the job was going to see a boxing academy in Kilburn. I suddenly had this blinding flash that maybe this was a sport that wasn't being sufficiently encouraged because it is a bit politically incorrect."

As we chatted about boxing, the name of Ricky Hatton came up. Boris said he had never heard of him. "I love watching them biff each other but I don't really know who they are." One personality he has heard of, though, is Dwain Chambers. Just.

"Now wait a minute – the guy who's cheated? Took drugs? Right?" So should Chambers be allowed to go to Beijing? "Absolutely not. No, I would not be happy about that. It would send out all the wrong signals."

Johnson says he sees sport as an essential weapon in fighting the Asbo culture. "I'm not suggesting it's the whole solution. This is not just some crazed playing-fields-of-Eton type of thing but it is something that inspires me and makes me feel there is real scope for expanding it into evening out the differentials and injustices in London.

"I am really sad that competitive sport in this country has not been encouraged as much as it should be. These school races where nobody was allowed to win, how ridiculous – a load of bollocks. At school I wrote something for a posh essay society about the importance of sport as a way of getting people to feel better about themselves, that sort of stuff. I remember it was derided by the headmaster but basically it is true."

The former mayor of Athens has advised him that his main task for the Olympics must be to get London enthused about them. Does he agree? "Oh, deffo. Absolutely." And tomorrow, London 2012 will outline the pivotal role he will play in Beijing on 24 August when the Olympic flag is handed to him by his Chinese opposite number. Perish the thought he might drop it or wave it aloft while declaring: "Long Live Free Tibet". For while "Bojo" might have some fun with the Games, he obviously takes sport seriously, and hopes sport will return the compliment.

Bojo speaks his mind

'Everyone is worried we are going to waste squillions on projects that are going to have no lasting benefit'

On budget concerns for London 2012

'It takes you back to the terror you experienced. You remember diving in, fearing your trunks might come off'

On his enjoyment in watching school sport

'These school races where nobody was allowed to win, how ridiculous, a load of bollocks'

On the role that sport can play in society