If politics were an Olympic sport, would Boris Johnson get the gold medal? As he welcomes the world to London for a festival of corporatist hypocrisy and athletic achievement, the mayor is in the middle of running his own long-distance race, which he hopes will conclude with Boris crossing the finishing line in Downing Street and ascending the winner’s podium on the steps of No 10.

Ignore any claims made by Johnson that he has no intention or chance of becoming prime minister. In television interviews he now struggles to keep a straight face when he is asked the question. “I have as much chance as being reincarnated as an olive,” he said in one. He goes on to quote Michael Heseltine claiming he “can foresee no circumstances” in which he would run for the top job. That was the cynical form of words Hezza used as he waited for the right moment to remove Margaret Thatcher. In reality, Boris is one of the most all-consumingly ambitious men of his generation and his denials are, to borrow his own colourful phrase, an inverted pyramid of piffle.

There are sizeable hurdles in his way, of course. Some Tories and former colleagues are determined that Johnson should never win the race to be Conservative leader. Instead, they would like him to be for the high jump. “Shallow, duplicitous, selfish, sociopathic, scheming,” says one usually generous-minded ex-colleague when I mention that I am writing this piece on Boris’s prospects. I had asked him to define the man in five words. Another laughs and then comes up with: “Infuriating, lazy, funny, charismatic, brilliant.”

But it is no longer only Boris who takes seriously the idea of Boris becoming Tory leader and prime minister. One sensible Tory donor muses: “Perhaps if Cameron does not get his act together we will go for the one with the hair. Boris has something special, he connects with people. He has star power.”

A Tory colleague who rates him highly says that he has long thought of Boris’s career as having five stages. “We are now on stage three. Stage four involves him being prime minister and in stage five he becomes president of the United States.” (He was born in New York, when his father was a student.)

Another MP pondering the possibility can now envisage him becoming Tory leader, perhaps: “He has flaws and people like that they are obvious. They see that he isn’t smooth and didn’t come from the political production line. If times are good you can see people giving him a whirl. But would you bet your house and your mortgage on him in an economic crisis? No.”

That sense that Boris is fun but unserious, and potentially even dangerous, is the greatest impediment to further advancement. The thought of him being handed the nuclear codes is not a prospect likely to reassure any wavering voters.

And yet, for all the doubts, he has built what it is customary these days to refer to as an extraordinarily potent “brand”. When the idea of a run for mayor was first mooted it seemed initially like an in-joke cooked up on the comment desk of the Daily Telegraph. Boris being MP for Henley seemed about right, but could he possibly win over millions in a city as diverse as London? It seemed an unlikely prospect.

Guided by the Australian strategist Lynton Crosby, who made him cut his famously mangled mop of hair and avoid obvious gaffes, he defeated the veteran Ken Livingstone, that odious but cunning embodiment of the London Labour machine.

The first term of his mayoralty was a curious affair. In the 2008 campaign I wrote in the Daily Telegraph in support of Boris, describing him as a cavalier to Livingstone’s joyless politically correct roundhead. In office the new mayor was certainly hugely entertaining, but other accomplishments were harder to quantify. There were those grey and blue bikes which appeared on the streets of London, although there was always a suspicion that he had inherited a good idea from Ken and then made it his own. Beyond that, even those who voted for him would struggle if they were put on the spot and asked to list his practical achievements.

Curiously, the existence of this policy void, coupled with yet more scandal in his convoluted private life, does not seem to have done his reputation the slightest bit of harm. Despite strong Labour leads nationally and in London he won his re-election bid, somehow floating above the standard fray, categorised as a celebrity and amusing character who can reach parts of the electorate which conventional politicians struggle to get near. There are parallels with the SNP’s Alex Salmond, another big figure whose public reputation is that of the jovial populist, when in reality, just like Boris, he is single-minded and driven to the point of monomania.

In Johnson’s case, the books and highly entertaining columns (“like shaggy dog stories written by Cicero”, in the opinion of another former colleague), appearances on Have I Got News For You, rugby tackling of opponents on the football field and assorted outrages have made him into the clown prince of the anti-politics movement.

Ask a Tory MP, peer or commentator with teenage children whom their offspring have been most impressed by hearing they have met and there is a fair chance that they will answer with one word: Boris.

For all the forced attempts at bonhomie, such fame does not endear him much to David Cameron or George Osborne. I was standing nearby when, shortly after Boris’s triumph in the first mayoral election, the new mayor swept into the room. The Tory leader was elbowed aside by photographers keen to get a picture of the blonde bombshell. Cameron, who is good-natured but ultra-competitive, looked a little put out at being so obviously upstaged.

Cameron and Osborne seem fascinated by the Boris phenomenon, in the way that medical researchers are fascinated by the emergence of particularly virulent new strain of a disease which poses a serious threat to public health. Both make a not terribly convincing show of trying to appear relaxed about his rise, with the prime minister often wearing a forced smile whenever he and Boris are together on the campaign trail. The Conservative leadership wanted him to win re-election, of course, because defeat would have suggested that the Tory tide was going out. They also know that if he had lost Boris would have returned as rapidly as possible to the Conservative benches at Westminster and become a more immediate threat.

As it is, they now know he is committed across the river at City Hall until his term finishes in 2016, or at least they think he is. If Boris can find a way of getting a seat at the next election, and combining it with the tail end of his mayoralty, he will surely do so.

For the chancellor, whose leadership ambitions have been dealt what should be seen as a fatal blow by the disastrous reaction to his recent Budget, the eventual return of Boris will be problematic. Osborne cannot be leader. At a gathering of normal non-politically-obsessed people, try mentioning the thought that he might one day hold the top job and watch the reaction.

That means the chancellor’s best hope after Cameron is to try and become a king-maker and then retain his exalted position in the hierarchy. He may have to choose between backing Boris or gambling on a rival such as Education Secretary Michael Gove being strong enough to win by that point. Other Conservatives, from the excellent last two parliamentary intakes, may by then also fancy a run at the leadership, pitting Boris’s star power against their earnest and commendable hard work on policy and ideas. None of this wrangling is as far off as it might sound. If Cameron loses the next election the Tories will be choosing a leader three years from now, and even if he wins he is determined to avoid going on much beyond the middle of the next parliament.

His critics frequently say that Boris has no discernible following in the parliamentary Tory party, but many MPs care most of all about holding on to their seats. If there is a sense that enough of Britain buys Boris, then when the moment comes there will be MPs who sign up.

The danger for the country, and the Tories, is that all of this is seen through the prism of celebrity and personal ambition, when there are such vast economic, constitutional and cultural challenges confronting the nation.

Before this year’s London elections Cameron and Osborne let it be known that when Boris joined them for a private dinner in Downing Street, just months before he was due to face the voters of London, they asked to hear his plans for the looming battle with Livingstone. What they heard — a bit of bluster and a very thin policy prospectus — horrified the prime minister and chancellor. There is a certain irony in the architects of the Conservative party’s inept, but very expensive, campaign for the 2010 general election accusing Boris of lacking any clear worldview or retail offer, in the policy jargon. But is there really any more to him than funny speeches and a hunger for power?

“I have no idea what he believes in other than himself,” says a prominent Conservative. Above all it is clear that Boris believes himself to be a man of destiny. In the mid-1930s the prospect of Winston Churchill becoming prime minister was not taken seriously until circumstances changed. Boris, says a sympathiser, sees it in similar though less dramatic terms, and one must hope fervently that any moment of destiny does not include the need for military conflict. But it is perfectly possible that Boris’s run for the Tory leadership in the middle of this decade would coincide with Britain attempting to work out, after the eurozone crisis, what a redrawn relationship with Europe will look like. To Boris, the idea of Britain as great global trading nation which has good but much less restrictive relations with Europe is appealing. That may be where British public opinion ends up too.

The most appealing aspect of Boris Johnson’s credo is his view of government. It seems Rooseveltian (Teddy, not FDR) in its conception, something he shares with Michael Gove. Too many modern Conservatives now sound as though they hate government and all its works. Even if the state is shrunk, as it must be to create the space for private endeavour to flourish, there will still be a lot of government. Must it be talked of in abusive or wholly negative terms?

Johnson is a free-marketeer but he is also comfortable with government using its clout to order large projects which are Victorian in the scope of their ambition. Instead of wasting years on Heathrow, and making life intolerable for those living in south-west London, he thinks it would be far better to create the best airport in the world with four, five or six runways and fast rail links into London from the edge of the Thames estuary. “Boris Island”, which is much more likely to involve building on the coast than the construction of a new island, dwarfs David Cameron’s rather limited plan to take 25 minutes off the journey time between Birmingham and London with a high-speed train line. “We have to have a new airport” he told New York magazine. “One of the only reasons I want to assume supreme power in England is to make sure that happens — for God’s sake, don’t quote me saying that.”

As with everything involving Johnson there is a large element of risk involved. He may yet exceed the voters’ capacity for amusement. His timings may be derailed by another economic crisis or the emergence of a strong Conservative rival. But don’t bet against Boris.