But what is the Tory Party centre-right, modern and technocratic about that centre-left, modern and technocratic New Labour isn't? Able figures such as David Willetts, who will shadow David Blunkett, find that New Labour is as unafraid of change in office as it was in Opposition.
In education, it is giving schools more power over their own affairs and pushing back the monolithic LEAs. It is introducing elements of selection in order to raise standards. This is coyly called "specialisation", which is rather like calling a spade a soil-displacement implement.
Mr Willetts has long been in favour of these ideas. So how is he to respond when New Labour does what the Tories have been asking them to do? Other ministers will have the same problem.
The Government is constantly reforming and refining its ideas - as well as ideas that have become the lost property of the Conservative Party.
The lumpen Tory mind has one answer to this - namely to call for a more ideologically pure version of whatever policy the Government is pursuing. At this point, the tactical argument is lost, since the public concludes that New Labour is the party of moderation and the Tories the bog-eyed ideologues.
Mr Hague would not be the former McKinsey management consultant man he is if he were not aware of this danger. He knows he still has a vital question to answer: what kind of party do the Conservatives want to be? True, he now has some better brains at the top table to help him answer it. Mr Willetts and Francis Maude are high calibre. Behind her comic self- effacement, Ann Widdicombe is a sharp cookie.
From these parts, Mr Hague must begin to forge a whole. The outgoing shadow cabinet was less a choir than a loosely orchestrated ensemble. If there is an esprit de corps and a shared sense of purpose, it has not been visible to the naked eye.
There are two possible responses to electoral disaster. One, favoured by Mr Blair when he led Labour in opposition, was to admit that the party and the electorate had parted company and set out to rebuild the relationship from scratch. The other, to which many Tories are still prone, is to assume that it was only the high policy division of Europe that caused the Stalingrad; so unite behind a new leader and carry on as before.
But the assumptions of old Conservatism will no longer suffice to regain power.
The old ties of mythical Toryism have frayed. The sanctity of the Commons, the House of Lords, the way the United Kingdom is built and wired, the electoral system, are all under assault. To their horror, the British public does not really care as long as their taxes do not have to pay higher taxes for these schemes.
The Conservative Party needs to reflect a country that is more flexible and less attached to the trappings of tradition than it is. It cannot afford to lapse into moral fundamentalism, nor convene itself as a kind of libertarian cabal. Most of all, it needs to make itself attractive to the William Hagues of tomorrow - who are meritocratic and unemcumbered by snobbery, rigidity and Carlton Club sexism.
In order to make his party re-electable, Mr Hague has to take on the prejudices of many of his own party members, who see nothing wrong with their world view and are constitutionally unsuited to a climate of change. That is a Kulturkampf to make Mr Blair's Clause 4 fight seem like a minor skirmish.