Tony Blair is known to have mused that "personalities" might ultimately "do" for his government. And the most enduring and endlessly fascinating personality conflict at the heart of the New Labour project is deemed to be that between Mr Blair and his "Iron Chancellor" Gordon Brown.

Although the honeymoon is well and truly over, the country is nowhere near concluding that it no longer likes the Blair administration. We have long known, however, that New Labour's ruling elite don't much like each other.

Gordon and Robin (Cook) may have mended their relationship, but only after years of silence. John (Prescott) makes alliances as and when he can, but probably doesn't care much more for Gordon, Robin or Stephen (Byers) than he does for Peter. And for all public appearance to the contrary, close observers think the Brown/Mandelson wounds have never really healed.

Mr Mandelson may first have tipped Gordon Brown as the likely leader of the next generation, but as Hugh Pym and Nick Kochan note in their biography of the Chancellor, the respect never seemed wholly reciprocated. A former Brown aide told them: "Although Gordon worked with Peter, he never trusted him. I remember him saying early on, `Watch Peter, he'll do us in'."

Mr Mandelson will never shake the belief that it was the Chancellor's former spin doctor, Charlie Whelan, who did for him with the revelations of that home loan from the Brownite Geoffrey Robinson, which forced his ministerial resignation in December 1998.

Mr Whelan is reportedly back in play, amid renewed signs of Treasury briefing against Downing Street - and vice versa - following last week's admission by the Prime Minister's spokesman, Alistair Campbell, that the tax burden has risen under Labour.

Every such spat is a potent invitation to the press to focus again on the perceived faultline at the heart of this government - the Chancellor's continuing belief that he was cheated of the succession following John Smith's death.

Dark, broody, brilliant, brusque, sometimes rude, volatile and explosive, Mr Brown was reportedly reduced to tears by repeated suggestions - attributed to Downing Street briefers - that he was "psychologically flawed". The author of that comment will know that Mr Brown is not a man lightly to let go a grudge. And the very suggestion betrayed the certainty of the Blairites that the Chancellor most definitely has not abandoned hope that the leadership will ultimately be his.

Hence, to an almost absurd degree, the Chancellor's Budget this afternoon will be scrutinised, as much for what it tells of his accumulation of power and his future ambitions, as for the economic health of the country and its relationship to Labour's already sunny re-election prospects.

In a brilliantly subversive piece in the Observer recently, Andrew Rawnsley charted Mr Brown's emergence as Britain's "virtual" prime minister, casting Mr Blair as a victim of the myth that he had created a presidential system of government: "There is a concentration of power at the top, but the master controller is not Blair. It's Brown. Under the aegis of his spending reviews, and by tying departments to his performance targets, the Chancellor has made every other minister accountable and beholden to the Treasury. He whistles; they beg."

It may well be that the concentration on work and welfare rather than health and education reflects Brown's priorities. It is true that he will write the key elements of the manifesto, and have a controlling influence in what a second Blair administration will and will not do. It is Brown, crucially, who will decide whether the economic criteria for joining the euro have been met.

But it is fanciful to think everything he does is with one eye on the possible succession, or that his influence derives merely from Blair's lack of grasp of the economic detail.

The notion of Blair the president and Brown the effective prime minister - the former the chairman, the latter the chief executive of UK plc - undoubtedly upsets Number 10. But many observers think it close to the reality - and, moreover, one that has served Blair and Labour well.

One of the sharpest commentators in British political journalism says of Brown: "Lurking behind that huge ambition, there is bound to be some envy, not least because Brown is the more substantial thinker."

This tribute to Brown acknowledges that he has been a powerhouse in the creation of the New Labour project, the man who reworked Labour's economic policy to make it acceptable to Middle England. Moreover, he adds: "Brown did a lot of the hod-carrying and bricklaying, while some others were concerned only with the facade."

This afternoon, Mr Brown - son of the Manse, and lover of prudence - will again be found bearing the load, laying the foundations for what Labour fully expects will be the reward of the first full second term in the party's history. Tony owes him - and they both know it.