The more intriguing and consequential divide is between the two New Labours that have emerged from the 1997 victory. The struggle between them will determine what this government achieves, the kind of Britain Tony Blair leaves in his wake, as well as who and what succeeds him.
The first wing we shall call Earnest New Labour. It is inhabited by believers in a centre-left revolution - radical decentralisation, electoral reform and more daring loosening of the constitutional corsets. Its prayer wheel is the Third Way. It seeks - in the words of Mr Blair's recent pamphlet - "a modernised social democracy" and believes in an extensive freedom of information Bill. Its natural adherents are the boyish intellectuals of the No 10 policy unit and related think-tanks.
The second - and it would squeal at the description - is Conservative New Labour. It owes more to the philosophy of civic conservativism articulated by thinkers such as Michael Oakeshott than tired old social democracy, which keeps producing governments in Europe without producing ideas to go with them.
It is lukewarm about devolution and solely concerned now with destroying its unwanted offspring - the rise of Scottish nationalism. Sceptical about electoral reform, Conservative Blairites back the alternative vote rather than proportional representation, for no more idealistic reason than that AV is the system that most comprehensively stuffs the Opposition. Mr Blair might talk a big social democracy, but he governs with the shrewd and cautious instincts of a managerialist. In his calculation of how to maintain and expand the party's grip on power, he has the old Tory instinct of being the natural holder of power. Conservative New Labour's only concern about freedom of information is how to water down the promised Bill to the consistency of consomme.
Margaret Thatcher, as so often, is the dividing line. Mr Blair's colleagues from the Earnest tendency think she did far more harm than good and still refer in high emotion to "wasted Tory years". They would rather have had bad Labour government than none at all. Gordon Brown carries their torch, flanked by Robin Cook, Margaret Beckett, David Blunkett and Clare Short.
Labour's New Conservatives, Peter Mandelson and Jack Straw foremost among them, have stealthily inverted this view, to the extent that Mr Mandelson spoke in Blackpool of the "lot of pluses" about her reign. The rising tribe of ambitious ministers - Stephen Byers and Alistair Darling spring to mind - are falling in behind this revisionism.
New Labour Conservatives love the macho language of "zero tolerance" and - as Jack Straw has shown in his introduction of draconian anti-terrorism laws and now in his proposal to expand the asset seizure from suspected criminals - are a bit careless when it comes to civil rights. One enjoyable result of this is an inversion of the laws of nature to cherish - Friday's Daily Telegraph attacked a Labour home secretary for being too tough on criminals.
Earnest New Labourites regard Mr Blair's embrace of the middle classes as a means to keeping power in order to enforce a radical programme of reform. Conservative Blairites do not see the satisfaction of the middle classes as a means to an end, but as an end in itself.
Mr Mandelson was traduced for his comments about the "working-class, horny-handed, dirty-overalled people", proving that irony is a risky pursuit for a politician. But the substantial point that this most Conservative of Labour politicians was making is that New Labour is in the process of jettisoning any residual identity as the natural home of the working man or woman, and that it has developed a rather brutal, meritocratic streak which makes it appeal to aspirant types.
Contrast this with Mr Brown's documented doubts about meritocracy, and his attachment to the notion of equality and the redistribution of opportunity as a prerequisite of the redistribution of wealth.
Can the Conservatives (the Tory ones I mean) draw any comfort from this contrast? Not for now. The immediate consequence of New Labour's ideological divergence is that it can do whatever it likes, taking ideas from across the spectrum.
Leaving aside the question of Britain and Europe, where the rules are different and the game, for both parties, a far longer one than commonly acknowledged, it is now virtually impossible to think of a policy that New Labour would deem to be too Tory to consider. I stick to my prediction that after two terms of Mr Blair's government, we will have had a radical restructuring of education and the health service.
So William Hague's attempts to place anything clear and blue between himself and the Government are in vain. How much more appealing to business can you get than the Secretary of State for Trade and Industry? How much more stentorian than the Home Secretary? Even the Earnest Chancellor is a Conservative on the economy.
So instead of asking whether the Tories are right or wrong, we find ourselves asking what the point of them is at all. One of the sadder vignettes was the appearance of Michael Howard on the Today programme complaining that, as shadow foreign affairs spokesman, he had not been allowed to give his views on Kosovo.
Poor Mr Howard: unable to escape his previous convictions. Like an old lag, he is fatally associated with the policies he imposed in office when he is trying to go straight and do some useful community work.
It is getting difficult to find a Tory who is not in a state of envious love with New Labour. Michael Portillo's recent TV preen-in with Peter Mandelson convinced me that the two were separated at birth. Any hopes I had of picking over Labour's conference in the bar late at night with gimlet-eyed Tory observers were dashed. They all think Tony is brilliant. Disillusionment with their own gang has produced an excessive admiration of their old enemies. The Tories are not functioning as a shadow anything - except of their former selves.
In the long run New Labour's two tribes will fall out. They will do so because they have entirely different ideas of what would constitute success and failure for the Blairite project and how much equality it is supposed to deliver to whom. One side will triumph and the other side will cry treachery. But for now they are at peace: united in thrall to a chieftain who represents what each of them wishes to see. It is a magnificent illusion.Reuse content