So, what is he up to?

What was that all about, then? It was almost as if Tony Blair fell out of a door into the street, tie askew, shouted incomprehensible words at shadowy figures in an upstairs window, then retreated, slamming the door behind him and leaving us, the people in the street, looking at each other and wondering what was going on.

What was that all about, then? It was almost as if Tony Blair fell out of a door into the street, tie askew, shouted incomprehensible words at shadowy figures in an upstairs window, then retreated, slamming the door behind him and leaving us, the people in the street, looking at each other and wondering what was going on.

This confusion was partly because so many things happened at once, in the space of a few hours late on Thursday night. The Prime Minister announced he was going into hospital; that he wanted to serve a full third term if he won the next election; that he would not contest the election after that; and that he had bought a house to move into when he left Downing Street. Then the result of the Hartlepool by-election was announced.

Four of these five things were important. The one that was not was the front-page lead in the Daily Mail and the Daily Express the next day: "Blair Heart Shock". The headline-writers would have done better with "Blair Heartlepool Shock", because Labour's victory there was a more significant pointer to the future. If Iain Wrighthad lost, then it might have been legitimate to ask whether Blair was the right leader to take Labour into the general election. As it was, the story immediately changed from "test for Blair" to "disaster for Howard".

The heart operation provided the excuse, though, for Blair to make two other announcements. One was that he and Cherie had bought a house in Connaught Square, and the other was to give the delegates who chanted "four more years" at his party conference speech what they wanted.

The heart business Blair can shrug off. All the consultant cardiologists the BBC can find are agreed that it should make no difference to his work rate. The curious venture into the buy-to-let market is harder to explain. Why should the Prime Minister's family borrow a lot of money to buy a house into which they have no intention of moving for nearly five years? It was the house, not the heart, that required the delivery of the third-term pledge in triplicate to the political editors of the BBC, ITV News and Sky, for whom Blair recorded consecutive interviews on Thursday.

Yet the declaration of intent to serve a full third term does not answer the question of why the Blairs bought the house. The explanation, I think, is that Tony and Cherie started looking for a house in the spring. The Independent reported yesterday that they had exchanged contracts some time ago but delayed completion for three months. That allowed a Downing Street official to tell me truthfully that they had bought the house "very recently", when the important date is when they made the decision to buy. That would seem to be around April, which happens to be when a succession of cabinet ministers urged the Prime Minister to stay on, and when John Prescott made his comments about the plates moving. They all seemed to take seriously the possibility that Blair was planning to step down later this year - that is, around now.

Indeed, nobody I have spoken to denies that Blair gave a pretty strong indication to Gordon Brown, in front of Prescott acting as a kind of notary, that he would step down about now. Nobody, that is, apart from Blair himself in public, who has dismissed it as "absolute rubbish" and said that "you don't do deals about jobs like this". But he has to say that.

He has to say it, not least because of the reasons why he decided not to stand down after all. The Prime Minister's friends are furious about the Chancellor's disloyalty. Their version is that Blair asked Brown for his support over the past year, to get him past the top-up tuition fees vote and the Hutton and Butler reports, to hand over power in Iraq and put the five-year plans for public service reform in place. Then Blair would feel that he had secured his legacy.

But they say that Brown has failed to keep his side of the bargain. He was obstructive over top-up fees, and he fought the five-year plans, opening up what one of the Chancellor's advisers was happy to declare to me last week was a "huge ideological divide" at the top of the Government. Although the two big ones, health and education, have been settled in a set of compromises that satisfied neither Blair nor Brown, there is still a lot of shouting and crockery-smashing audible behind closed doors. In particular, the five-year plan for the Department for Work and Pensions has been delayed because Blair wants to get more of the large numbers of older men on sickness benefit back into work. I suspect that was the secret story behind the resignation of the Work and Pensions Secretary, Andrew Smith,last month: the Chancellor may have felt that it would be unhelpful to him for a known Brownite to have to drive through controversial reforms.

Brown is "like a child reaching for the sweets on the top shelf", according to one of Blair's friends. He can't stop himself pulling everything down in his impatience to reach the prize. Brown's friends are just as rude about the Prime Minister's slipperiness. They say Brown was tricked into being what he regards as supportive, only to be betrayed by Blair yet again. There can surely be no doubt any more that these views reflect accurately the feelings of the principals towards each other. Brown was asked in an interview published last weekend whether he considered that Blair had betrayed him. "I'm not going to answer that," he said. "It's not helpful."

That is one reason why Blair decided to carry on. There are two others. One is that to go now would look like an admission that he had got it wrong in Iraq. The other is that he can. The significance of the Hartlepool by-election is that there is nothing to stop Labour coasting to - an admittedly apathetic - victory at the general election. Blair may be a liability to his party, in that Labour could get some votes back from the Liberal Democrats if Brown were leader, but he is not enough of a liability to force his party to get rid of him.

The remaining puzzle of this seismic week in politics, therefore, is why Blair put a time limit on his tenure of office. A consensus seems to be emerging that this was a big mistake, a classic case of Blair managing headlines at the cost of long-term problems. I'm not so sure. Simply repeating his intention to serve a full third term would have been treated with the scepticism it deserved. He does not expect to last that long himself, so by setting himself a deadline beyond his likely departure date, which is currently 2006 or 2007, he hopes to push the speculation back.

Thursday night provided a glimpse of the turmoil that lies behind the blank façade of public politics. But the door is shut again, and we can only guess at the bruises and recriminations still carrying on out of sight.

John Rentoul is the author of 'Tony Blair: Prime Minister', published by Time Warner