John Rentoul: Last week, I asked how far Alan could go. Today, Gordon must be wondering, too

The rise of Alan Johnson continues. Last Sunday this column noted how well placed the new Secretary of State for Education is to win the deputy leadership of the Labour Party, and wondered why he should stop there. Three days ago, a transcript of today's pre-recorded interview with him on GMTV was published. In it, he says that people have asked him if he would be interested in the deputy leadership when there is a vacancy. "And I've said quite honestly, 'Yes, I would'."

Johnson's interview was not only pre-recorded, it was premeditated. I am told that he had discussed with colleagues what he would say - and as you can see it is not as if it had to be dragged out of him. So it is worth analysing his calculations.

It seems unlikely that his expression of ambition was designed to destabilise John Prescott. Prescott has done enough of that himself, and clearly intends to stay on, both as deputy leader and as Deputy Prime Minister, for as long as Tony Blair is there.

It is more likely that it was planned as pre-emptive self-promotion. Johnson has learned the lesson of the recent history of Labour leadership contests. In 1992 there was a rising Labour politician who thought about standing as deputy leader when Neil Kinnock and Roy Hattersley resigned. His name was Tony Blair. Another rising Labour politician called Gordon Brown sought to dissuade him; Peter Mandelson and his wife Cherie urged him on. While he pondered, John Smith, the clear favourite for the top job, pushed forward his preferred choice as deputy, Margaret Beckett. She was less of a threat to his own position than Blair would have been and, once Smith had made his preference known, she carried all before her.

By announcing his interest in the deputy leadership, Johnson has inhibited Brown in signalling his support for a rival candidate. The Chancellor was already looking benignly on Harriet Harman's early run. Now that Johnson has gone public, though, he has momentum and it is hard to see who could stop him winning.

In American political terms, he is a candidate who has biography. The standard way to launch an election campaign in the US is to run a 60-second commercial using the story of the candidate's life to project his or her values. Johnson's would pack a real emotional and ideological punch. Orphaned at 12 and cared for by his older sister; left school at 15; became a postman and a father of three by the age of 20; the youngest leader of the postal workers' union before becoming an MP in the 1997 landslide at the age of 46. As a minister he is New Labour with a working-class accent. And he has a sense of humour. With Charles Clarke he was part of a charm offensive to get tuition fees through the Commons: "I did the charming and he was offensive," he said.

That, then, is the deputy leadership decided. Last Sunday, Johnson's potential was plain. The only question was whether he wanted it. Well, now we know.

The next step is to transpose all these calculations up a scale, and apply them to the question of the leadership itself, and therefore to the office of Prime Minister. The first objection that one used to hear to the suggestion that Johnson might be the "stop Gordon candidate" was that he was "lightweight". But I remember when the same word was used to explain why Tony Blair could never be Labour leader. The question is not, is he lightweight, but has he put a foot wrong?

Johnson should not be taken at face value when he protests that the deputy leadership is the limit of his ambition. He told GMTV that he had once said that "the idea of getting me into No 10 was like the idea of putting the Beagle on to Mars: a nice idea but doomed to failure".

True, the odds are still against it. But they have shifted since last weekend. The reason John Smith didn't want Blair as his deputy are the same as the reasons Gordon Brown doesn't want Johnson: it could be a base for the next stage. This time, though, there is still some time to go before the top job becomes vacant; meanwhile, merely being considered for the deputy leadership opens up the possibility of running for leader.

For some time, the certainty of Brown's succession has been self-reinforcing. The fact that a candidate for either leader or deputy needs to be nominated publicly by 45 Labour MPs has made it difficult to see how Brown could face a contested election. That would require 45 MPs to announce, in effect, that they have no interest in holding office in a Brown government.

There was even talk until recently of the Chancellor subcontracting some of his supporters to a hopeless hard-left candidate simply to ensure a contest, because some of his supporters realised that it would not be in his interest to move into No 10 without a vote.

If Johnson ran for the deputy leadership, however, he could do what John Prescott and Margaret Beckett did last time, and run for the leadership too. Then he could get 45 nominations for the top job - an unlikely coalition at first, perhaps, of the Campaign Group left and the Blairite ultras. Merely preparing to run for deputy means that journalists, MPs and activists discuss your suitability for high office, and a wave builds if there are no rocks on which to crash. It all depends on the opinion polls. The polls continue to suggest that Brown as leader would fail to lift Labour against David Cameron, the smoothie chops of Desert Island Discs.

Of course, we do not know yet whether Johnson would do any better, although the story of the working-class London boy with no O-levels up against the Eton- and Oxford-educated Cameron has a certain built-in narrative drive. The last time a polling company asked people who should take over from Blair as Labour leader, it didn't have Johnson on the list. Last week a lot of people heard about him for the first time. Over the next few months, his tenure at the Department for Education will introduce him to many more - and his performance is likely to be compared favourably with Ruth Kelly's. And the moment Brown's succession stops being certain, the future could flip. The postman jokes have started already. Knock, knock. Who's there? Gordon. Gordon who?

Last week, The Spectator under the new editorship of Matthew d'Ancona, the Blairite-turned-Cameroon, mischievously put the following headline on an article that did not quite say as much: "Alan Johnson is the Labour leader that Cameron's Conservatives fear". But if that headline were to become true, Gordon Brown's long-nursed ambition could collapse into an even deeper black hole than Al Gore's when he failed to win the US presidency.