John Rentoul: Who do you think you are, Boris Johnson?

Worryingly for David Cameron, the increasingly transparent reply from London's mayor seems to be 'a future prime minister'

There is a simple reason why Boris Johnson, the Conservative Mayor of London, described David Cameron's view that ours is a "broken society" as "piffle" last week. It is that Boris is in power, and Dave is not.

In opposition, politicians say that "our country today" is "unfit for any decent person to raise a family and live in". That was Tony Blair, on his election as leader of the opposition in 1994. In power, he hotly denied that society was "broken". In his last six months as prime minister, he said that a spate of shootings of teenagers was "not a metaphor for the state of British society". Not at all. The problem was a "specific criminal culture among a specific group of people".

If Cameron becomes prime minister, his rhetoric will turn with the same certainty as the Earth about its axis, while Yvette Cooper, the leader of the opposition, will be praised by The Sun and the Daily Mail for her "courage" in describing much of urban Britain as reduced to "spiritual rubble".

Until then, Cameron lives in a "broken society". Boris Johnson, on the other hand, is in power. As he put it in an interview with Total Politics magazine last week: "I'm in government. This is government. This is government. This is big. This is huge. Huge, huge. This is bigger than my last job as a shadow spokesman by a factor of a hundred thousand." That was truth spoken off-the-cuff, and most revealing.

And the other truth, that Johnson typed himself with calculation aforethought in his Daily Telegraph column, is this: "If you believe the politicians, we have a broken society, in which the courage and morals of young people have been sapped by welfarism and political correctness. And if you look at what is happening at the Beijing Olympics, you can see what piffle that is."

On the radio and down the line from Beijing yesterday, Johnson failed to deny that he and Cameron disagreed, accusing John Humphrys of "trying to confect a pseudo row over a metaphor". He said that if anyone suggested Britain was broken in the sense that a washing machine was broken, in that it doesn't function at all, he disagreed with them. "It's not working terribly well, it's creaking a bit; it needs more rinse aid – there are things you can do."

The gap between power and opposition, then, is the simple explanation for the disagreement between the Conservative leader and the Conservative mayor. There is, however, a more complicated explanation that is every bit as interesting, which is that the Conservative mayor would like to be a Conservative prime minister. Since Johnson's election as mayor in May, speculation about his aspirations has been precisely that: conjecture. But I did notice a report last week by James Macintyre, The Independent's political correspondent, in which "friends" of Johnson spoke of his "ambitions to be prime minister" and his desire to "present an alternative to Mr Cameron".

Not that you really need to join the campaign to save Bletchley Park to decode Johnson's denials of any intent to use the London mayoralty as a stepping stone to No 10. In the past, he has said that the chances of his being prime minister "are about as good as the chances of finding Elvis on Mars, or my being reincarnated as an olive".

The "olive" line was so irresistible that it was even borrowed by Michael Gove, the Tory education spokesman, when he splutteringly dismissed the idea that his switch to contact lenses and ultra-Blairism meant that he had designs on the top job. (That was last August, when Gordon Brown was quite popular and there were rumblings about Cameron's leadership.)

Last week, though, Johnsonwent for a different joke. "Look, I really cannot foresee the circumstances in which I'll be called upon to serve in any such office," he told Total Politics. You do not need to be old enough to recall where you were on the day Margaret Thatcher resigned to spot the words used by Michael Heseltine to answer the same question with a vulpine smile.

"Honestly, my appetite for power is glutted," Johnson went on, with the next three words, "for the moment", so obvious that they did not need to be said. So obvious, indeed, that we hardly need "friends" of the Mayor to explain what he is up to, or sources close to David Cameron to confirm the Tory leader is wary of him – to put it mildly.

Dave and Boris both know that, like all the great inner-party rivalries of the past (Macmillan and Butler, Wilson and Jenkins, Blair and Brown), they are bound together but that their interests will diverge. Hence Johnson's muddle in the Total Politics interview over whether London is a testing bed for a Cameron government. "Bollocks," said Johnson. "The reality is we're working flat out for London."

Although he had just said: "The priority for us – and I think for the next Tory government – is tackling deprivation and disadvantage." And he went on to say: "Obviously I'm hopeful we'll do some things which will show that compassionate Conservatism can work in London and therefore can work in metropolitan areas across the country."

Tory leader and Tory mayor share an interest in the short term in Boris Johnson making a success of running London. But beyond that, their paths to No 10 go separate ways. Cameron has to do it the Blair way, as a parliamentary performer with no ministerial experience (except that he was an adviser, at the Treasury and the Home Office). He has to come in on words, promises and images.

Johnson, on the other hand, looks a little further to the future, after one or two solid terms as leader of a world city that is home to one eighth of the UK population. His route to Downing Street would be new to British politics, but is familiar in other countries. Jacques Chirac was mayor of Paris, for example, and many German leaders cut their teeth in state governments.

It is a gamble that would require a tricky re-entry to the House of Commons at the right moment. But Johnson has already confounded the doubters who thought his Etonian buffoon persona was a bar to serious democratic politics. As well as last week's interview with a political magazine (in which he compared Ken Livingstone to a "brooding pterodactyl") and yesterday's engagement on the Today programme, he also took part in BBC1's Who Do You Think You Are? on Wednesday. It was a virtuoso performance as the comic polymath, tracing his Turkish and Bavarian ancestry and at one point saying to a German archivist, "Ich habe der Mystery gecracked."

The London mayoral elections proved that his mix of sentimental nonsense about red buses and serious policy on youth crime could work in postmodern politics. And he could certainly be levered straight into the leadership of his party if events contrive a scenario where the Conservatives decide that they need his unusual brand of populism to win a general election.

Which is where his repudiation of the "broken society" gains a deeper significance. It may be one law of politics that society is always broken to opposition politicians. But it is another that optimism, uplift and looking to the future wins elections. Sometimes Cameron understands that, but he is inconsistent. Whenever he bemoans the broken society, he should have his first conference speech as Tory leader quoted back at him: "Let optimism beat pessimism. Let sunshine win the day."

But Johnson understands it better, because he is, as he says, "in government". If Cameron isn't careful, there may come a day when optimism will beat pessimism. In other words, when Boris will beat Dave.