After three weeks in the job, MrDorrell is fed up with questions about his cultural interests. Yes, he likes orchestral music, and yes he occasionally goes to the theatre, but his most abiding passion is ancient monuments. As for competing with Tony Blair's enthusiasm for rock music, he answers, with a smile: 'Do I look like a Rolling Stones fan?' It is a hot day in his Loughborough constituency but the minister is wearing a navy suit, a striped shirt and a sober, patterned tie.
Mr Dorrell's elevation to the Cabinet was one of the least surprising aspects of the reshuffle. He is the rising star of the centre-left who shone at the Treasury, impressing even the right with his presentational skills. But his arrival at National Heritage puzzled observers who thought him likely to be sent to Education, Health, Transport or Employment.
Mr Dorrell's pedigree is that of the minister given the impossible brief to defend, then pointed at the nearest television camera. He served as a junior minister at Health before becoming Financial Secretary to the Treasury and, in his time, did battle with Jeremy Paxman over the health service, the collapse of British membership of the ERM and Tory tax rises - surviving to tell the tale.
But National Heritage is different. It is about selling good news and getting positive headlines for initiatives such as the national lottery. Peter Brooke was once pictured with the rock group Right Said Fred. While keen last week to put down Mo Mowlam's idea of a 'People's Palace' for the Royal Family, Mr Dorrell has other ideas of the job: his style 'tends in the direction of developing a serious political argument rather than seeking media opportunities for their own sake'.
Educated at Uppingham and Oxford, where he read law, he then joined the family firm, which makes industrial clothing. It is based in his native city of Worcester, where he still has his main home, and has made him reasonably wealthy.
Worcester was also the constituency of his early mentor, Peter (now Lord) Walker, for whom he worked as a personal assistant in 1974. At 27 he had won a seat in the Commons but, decidedly not 'one of us', he had to wait eight years - some of it as Mr Walker's PPS (parliamentary private secretary) - before being promoted to the whips' office. Rebellious on social policy, he had the foresight to join the Guy Fawkes dining group; a fellow member was John Major. He believes in the 'active citizen' first championed by Douglas Hurd.
After a visit to a housing association in his constituency, he was waiting, sipping orange squash, in a Moroccan-style courtyard complete with fountain. Sitting under a sunshade, he argued in a precise, logical and polished way, dissecting questions before imparting his political spin. Tall, thin, looking younger than 42, he appears more relaxed in the flesh than on television.
His outlook on life is leftish: 'If we insist on reducing everything to economic minimalism, we diminish ourselves in our own eyes and in the eyes of the world. We have accepted for centuries that part of the cultural life of the country is stimulated through official action.'
He sees his new department as 'an expression of our common nationhood' and defends the principle of subsidy to minority arts such as opera. In January he made a speech, seen as a counterblast to his right- wing rival, Michael Portillo, in which he rejected 'the exaggerated histrionics of flag-waving nationalists' but spoke warmly of the nation's 'legacy of artistic achievements in music, literature and the visual arts which reflect our distinctive national viewpoint', which we 'should commit ourselves to pass . . . on, enriched, to our children'.
His decision to grant an extra three months to the Victoria and Albert Museum to try to keep The Three Graces in Britain - seen as alitmus test of whether he was going to be a 'toughie or a softie' - is consistent with this view. It should not, however, be read asa signal for the arts lobbies to open the champagne. The Evening Standard once said he stood 'about as far to the left of the Tory party as it is possible to do without falling off', but colleagues have noticed a move rightwards and an affection for Treasury orthodoxy.
In the next 12 months he will conduct a fundamental expenditure review of his pounds 1bn-a- year department - even though it has existed for less than three years. With the lottery due, in his estimation, to double the amount of money going to arts and sport, there is an opportunity to be more discriminating with its cash, while playing a national Santa Claus.
This windfall raises the prospect that Mr Dorrell could please the left of the party by channelling extra money to the arts and sport, and the right by cutting state subsidy.
Asked whether it is the responsibility of the state or the individual to fund libraries and museums, his response was Delphic. 'I would be anxious to ensure that we don't commit ourselves to doing something indefinitely in the future in the way that it has been done in the past. We need to reassess how our present pattern meets the cultural needs of the late 20th and 21st century.'
This is not, he stresses, tantamount to a plan to charge for public libraries, but 'what I am not committing myself to doing is maintaining each library building in the condition that it was left to us by an earlier generation'. And, as far as his wider review is concerned, he goes further: 'You have to be prepared to think the unthinkable merely in order to ask the relevant questions.' Whatever Mr Dorrell has in mind, some state funding is likely to be cut.
A series of controversial issues loom - cross-media ownership, privacy legislation, the British Library - and they will test the extent of his faith in the free market as against his commitment to preserving national institutions. Predictably, he is offering no hostages to fortunes, arguing that Rupert Murdoch has been a good thing 'because he has required the newspaper industry to address practices which prevailed 20 years ago which are wholly indefensible'. And, while he regards the BBC as 'an institution which had a tremendous tradition in a positive sense', he believes 'it also needed managerial change. I hope we can see a diverse media market'.
On the wider political spectrum, Cabinet colleagues are divided about how to counter Labour under Tony Blair. There are two schools of thought: 'Coke' (the Conservatives are the real thing, Labour a cheap imitation) and 'Clear water' (Mr Major must differentiate himself from Mr Blair through radical policies). Although he rejects the tag as simplistic, Mr Dorrell would back the first rather than the second; he believes the next election can be won if economic management reduces unemployment and presents the chance of tax cuts, while reforms on education and training are followed through.
Where does that agenda involve him? The fact is that Mr Dorrell has a big, challenging Cabinet job but it is not one that will influence the outcome of the election. 'There is,' he concedes, 'no point me pretending to you that people will choose to vote Tory because of our policy on the arts or sport. But that does not mean that they are not important.'