Whenever I used to see Sebastian Coe in his role as a minor Conservative MP or, more recently, as the dark-suited chief-of-staff to William Hague, I thought of the character Tom Buchanan from The Great Gatsby . Buchanan is a former champion athlete who is described, by the novel’s young narrator, as being ‘one of those men who reach such an acute limited excellence at 21 that everything afterward savours of anticlimax’.

Except that there was nothing limited about the sporting excellence of the young Sebastian Newbold Coe, even though much of his life since retiring from top-flight athletics must surely have savoured acutely of anticlimax. Coe was truly great - perhaps the greatest British athlete of the last century - and must have entered politics knowing that nothing he would ever do could recapture the intensity and grandeur of his sporting life; that the best of him, and long before his 40th birthday, was already in the past.

‘I won a marginal seat in 1992 and lost it in ‘97,’ he tells me when we meet. ‘In truth, I knew within 30 minutes of winning the seat that I would lose it again at the next election. Events were moving against us, and the arithmetic was unsustainable. Thirty six per cent of the vote in a three-way split was not something to base a career on. But I don’t agree that my life since I retired from athletics has been an anticlimax. No, not at all. If I pull this off, for example - well, this would be huge.’

He is referring to his role as chairman of the bid to bring the Olympic Games back to London in 2012. He was appointed following the surprise resignation in May of the previous incumbent, American entrepreneur Barbara Cassani. ‘This is the greatest challenge I have ever faced,’ Coe continues, with forgivable melodrama. ‘This chance will not come round again in our lifetime, and we must do everything we can to win. Bringing the games to London would leave such a powerful legacy, in terms of the environment, in terms of urban renewal and in inspiring interest in sport among so many children and young people.’

I am sitting with the good Baron Coe of Ranmore on a decrepit wooden bench at the British Airways Sailing Club in west London. Coe, who is tanned and wearing shorts, a white sports shirt and dark sunglasses, is waiting for Richard Branson and Rod Eddington, chief executive of British Airways, to arrive so that they can climb into a canoe for a publicity stunt to promote the London bid. BA and Virgin Atlantic are sponsors of the bid.

There is something remarkably boyish about Coe, who is 48 in September. He is lean, he moves quickly and his hair remains thick and dark. It is still easy to imagine him dressed in the white vest of Great Britain - and running very fast. ‘I still sometimes run more than 40 miles a week,’ he says.

The bid to bring the games to London has been blighted by the obligatory infighting (the resignation of Cassani and its subsequent fallout), by the alleged corruption of the bidding process (BBC1’s Panorama this week exposed how easily votes could be bought from members of the International Olympic Committee), and by prurience (Coe’s appointment coincided with tabloid gossip about a mistress and ‘late-night romps’ in his car).

All this had led me to expect that Coe would be anxious and harassed - an expectation reinforced when I received a call from his office, shortly before our interview, requesting that I ask him nothing about his private life.

What do you mean by his private life?

‘You know,’ the voice said.

I said that no, I did not know.

Then I discovered that a ‘minder’ from the London 2012 office had been assigned to sit in on our interview, as if to lead me not into temptation and the baron away from danger. But the minder, Fran Edwards, turns out to be very charming and Coe seems largely unconcerned by all the fuss. ‘I’ve been around a long time,’ he says, removing his sunglasses. ‘I was selected for the national athletics team at the age of 18, I was an MP for five years, I worked closely with William Hague - I’m too long in the tooth to worry about what the press are saying about me.’

He is perhaps being slightly disingenuous. After all, he unsuccessfully applied for an injunction to prevent his former lover, Vanessa Lander, from revealing the secrets of their affair in the Mail on Sunday in May - that, for instance, Coe paid for her to have an abortion while his wife, Nicola McIrvine, from whom he has since separated, was expecting their third child. ‘Seb was very unhappy about this story coming out when it did,’ one of his friends told me. ‘He felt there was nothing of interest to the public in knowing about what had happened in the past.’

The only problem with this explanation is that, at the time of his affair, Coe was a whip in a Conservative government led by a prime minister who, espousing a spurious puritan morality, was determined to ‘get back to basics’ but who turned out to be, like so many of his senior colleagues, an enthusiastic adulterer himself. The Conservatives remain stained by the scandal and corruption of the late Major years. Even Coe, who describes himself as necessarily ‘politically neutral’ in his present role, concedes that the party requires a ‘new narrative’. ‘Parties must understand,’ he says, ‘that it’s not simply that people’s aspirations change, but that the entire language of politics changes. When we were strong, the world was more certain. Politics was about the East-West divide and issues such as privatisation versus nationalisation. Now there are fewer certainties and perhaps we, the Conservatives, have not fully understood that.’

London is thought to be behind Paris, the favourite, and Madrid in the competition to stage the games. When the shortlist of five from which the winner will be chosen in July next year (the other contenders are New York and Moscow) was announced on 18 May, the IOC criticised many aspects of the London bid, notably the capital’s shambolic transport infrastructure. ‘But I don’t think transport is a negative for us any longer,’ Coe says. ‘In fact, I think it can become a real positive. I’m not here to win arguments about under-investment, over-investment or sideways investment in transport. What I am here to do is to provide a transport plan. Can I do that? Yes. Can I get 240 trains on 10 lines going into Stratford in 2012? Yes, I can. Can I get them in from Kings Cross in seven minutes on 15 shuttles an hour? Yes, I can. With the East London line in place, can I get them from Trafalgar Square into the heart of the Olympic complex in 15 minutes? Yes, I can. And I know that in eight years I can offer the best transport plan that has ever been put forward in an Olympic Games.’ Well, it’s useful, as Philip Larkin once wrote, to get that learnt.

Coe speaks with the smoothness and ease of the career politician. He is evasive when necessary, such as when I ask him why exactly Barbara Cassani resigned (friends of Cassani told me that she believed that London could not win, that she was disappointed by the lack of support from the government and that she disliked the forced affability of the Olympic circuit and the sycophancy that is necessary in the race to win votes), and has instant recollection of all the right statistics and supporting detail. He is effusive about the support of Ken Livingstone, and circumspect when discussing Tony Blair’s reported diminished enthusiasm for the London bid. ‘The perception may be that the Prime Minister isn’t behind us, but I know that he is absolutely committed. How do I know this? I’ve had private conversations with him.’

Coe is most animated when I ask him about the glorious summer of 1979 when, over a period of 41 days, he broke the 800m, the 1500m and the mile world records - the first athlete to hold all three records at the same time - and about fellow middle-distance runner Steve Ovett. His rivalry with Ovett, in the late 1970s and early 1980s, enthralled, enchanted and infuriated in about equal measure. It enchanted because they were so good; it infuriated because they refused to race each other outside international championships.

They could not have been more different: Coe was the intense, articulate graduate from Sheffield, coached by his father, Peter, and a model of middle class rectitude and stubborn determination. Ovett, from Brighton, was something of a free spirit, as audaciously talented as Coe but more naturally rebellious, which meant he was always more popular than Coe, perhaps because he appeared to care less. Together they redefined the art of the possible in middle-distance running, exuberantly winning Olympic gold medals, recklessly breaking world records. British sport had never seen anything like them, and never has since.

Today, Ovett lives in affluent seclusion in Australia while Coe remains a very public figure and quintessential establishment insider: politician, bureaucrat, ambassador, diplomat. It is fascinating to hear him speak about his great rivalry with Ovett because his recollection of it all is so startlingly fresh, as if he never ceases thinking about it. ‘I don’t think people ever appreciated how talented Ovett was,’ he says, with wonder his voice. ‘I’m not sure even Steve fully understood. Here was a guy who could win a national cross-country championship but also hold the English schools title at 200m. A week before he won the 1500m World Cup in 1977, one of the greatest runs at the distance of all time, he got bored and ran the Dartford half-marathon. He had phenomenal range, probably more than me. The only problem was he lacked confidence in his ability. I’m sure he could have run even faster, a lot faster, if he’d had more confidence.’

In 1988, Coe, age withering him, was left out of the British team for the Seoul Olympics, thus being deprived of a chance to win his third gold medal at consecutive Games (he won gold in the 1500m at Moscow, in 1980, and at Los Angeles, in 1984). ‘I would have won, I would have won,’ he says now of the 1500m final in Seoul, then gently raps his fist on the table. ‘You know, when I was left out, I was offered the chance to run for any number of other countries, including India, because one of my grandparents was Indian. But I couldn’t really do that, I couldn’t…’

There is doubt in his voice and you know that he knows that he should have accepted the offer to run for gold in Seoul, even if it meant draping himself in an Indian flag.

The Athens Olympics begin on 13 August. Yet never in recent memory has a British athletics team set off for an Olympics with such low-toned expectations, nor had so few individuals of national renown. Our champion sprinter Dwain Chambers is banned for taking the steroid THG, and the era of our dominance of middle-distance running is long gone. ‘I think track and field has a real problem because it’s such a tough sport to sell,’ Coe says. ‘We live in an odd culture now where you can go on Big Brother and become a household name. All this makes it that much harder for a coach to turn to a 14-year-old and say, “We think you’re very talented and if you stick at this, keep working hard, you might, by the time you’re 21, be making a few ripples on the pond.” Too many people want everything now and aren’t prepared to work. But the fundamentals of athletics - being able to run fast, jump and throw - are the fundamentals of all other sports. Master these and you have a chance at everything else.’

So can Coe bring the Olympics to London? If he does succeed, and the odds are against him, it would surely redeem all the disappointments of the recent past - the failure of his political career and the humiliating defeat of William Hague at the last election - and enable him once more to experience the adulation of victory. ‘To bring the Olympics to London would be much bigger than anything I achieved before. Winning an Olympic gold impacts upon yourself and your friends and family and, for a short time, your chosen sport. But this would impact upon the whole nation. It would be monumental, stratospheric.’

With that, he leaps up to shake the hand of a departing Richard Branson. He’ll have many more hands to shake before discovering whether he has won the longest and greatest race of his life.