Before we began our interview, I asked him what he might be putting up. He said he would love the portrait of Robert Owen by William Henry Brooke, one of his ancestors, but the National Portrait Gallery would not release it. He had tried once before when he was an education minister.
Then again, he could always hang something by his grandfather Leslie Brooke, a noted illustrator. Paradoxically for a charming and rather patrician Tory, Mr Brooke is the living embodiment of that long-forgotten 1970s slogan, 'the personal is political'. His main areas of knowledge and enthusiasm in his new portfolio are those which have involved his family, living and dead.
The visual arts are a long-held interest. 'Two of my sons took art at A-level.' So is sport. He is a cricket enthusiast and user of the House of Commons gym, but, perhaps just as important, 'my eldest son was president of the Oxford University Athletics Union'.
Questions on tourism, a hitherto unnoticed part of the National Heritage portfolio, lead as inevitably as questions on literature to Wordsworth's Dove Cottage in the Lake District. Mr Brooke sits on the board of trustees. 'My great-grandfather, Stopford Brooke, a Victorian preacher, bought it in 1890, five years before the National Trust was founded.'
Mr Brooke, 58, re-married last year. His wife, a 47-year-old Conservative agent, Lindsay Allinson, is a jazz fan. 'It's a wholly new area for me, and I'm enjoying it.'
Mr Brooke's father, Henry, was Harold Macmillan's Home Secretary, a frequent target of satirists, e g BBC-TV's That Was The Week That Was. But the BBC, awaiting the Green Paper on its future, can be relieved that Peter Brooke does not appear to be among its hardline critics.
It was not an area he would discuss in detail before the Green Paper, but when I said that his predecessor, David Mellor, had pronounced himself a liberal on the BBC, in favour of retaining the licence fee, he replied: 'I think you'll find I'm not a million miles from David on that.'
On other philosophical approaches to the arts, though, Mr Brooke and Mr Mellor are some distance apart. I mentioned Mr Mellor's recent forays against elitism and a speech in which he praised the classlessness of a National Theatre audience. Mr Brooke responded: 'I can understand why David Mellor took the view he did and I'm a profound believer in the liberating effect of art. I'm constantly struck by suddenly getting round to reading an author I've never previously read and the sense of immense pleasure at realising how good he or she was.
'But as for classless, it doesn't bother me per se to sit in an audience where people are dressed up. Actually I had never until this summer been to one of those son et lumiere concerts and sat in a deckchair. I hugely enjoyed it.'
Mr Brooke has already impressed senior officials with an astuteness behind the languid charm. It was, he says, an enormous surprise to be asked to take on his new job when he had just come back from holiday to vote in the Commons. 'Being asked to head the department was a surprise but also a pleasure. Nobody would construct their career this way round, but having six months off after 13 years as a minister you come back refreshed.'
But wasn't the department made for David Mellor, with his passion for the arts and sport? 'That's a question you will have to ask the Prime Minister. But I think this department is a wonderful idea. Inevitably, in a department as broad as this there are areas where any minister would be ignorant, but I have areas of interest. I'm a reasonably voracious consumer of broadcasting. But I don't pretend in-depth knowledge.'
What were his views on the Royal Opera House, the subject of two damning reports last week: 'Well, the Royal Opera House is in my constituency (City of London and Westminster South) and they have come to me for help in the past. That has been my relationship with it hitherto. But you have to be conscious of what kind of audiences are attending and it may be that access is decided by the level of ticket prices.'
Mr Brooke's constituency, like his family, has provided a sound introduction to the arts. 'I go to the theatre with a regularity that I hope all mankind does.' It must also help to have a constituency that includes all of the West End.
The visual arts are his abiding cultural interest (though he is keen to mention his love of churches, for which his department has some responsibilities). It is not just his ancestors that
engendered his love of painting. 'As a boy at school I was taught by a man who was passionate about painting, and you build on those foundations. I played both the piano and the oboe but never had anyone teaching me about music in the same depth, so I feel much more at ease with the visual arts.'
Asked about the future of the Arts Council, which the Government is pledged to review, Mr Brooke declares himself in favour of the traditional arm's-length principle of government funding of the arts, rather than having a powerful French-style minister of culture.
On tourism, he sees Dove Cottage as a model for others, hinting that it is the private sector that should boost tourism opportunities. 'People see what we've done in making Wordsworth come alive with no resources at all. It has been the creative energy of a group of people, not government.'
One of Mr Brooke's most controversial responsibilities will be to decide what action to take on privacy and the press. Would Mr Mellor's experiences influence him at all? He emphasised his strong belief in the freedom of the press - 'very much part of our heritage' - but 'I think there were plenty of features which a number of people might have found distasteful'.
In the coming months he will also have to introduce the lottery Bill to Parliament, and pronounce on the National Arts and Media Strategy drawn up by the Arts Council. He will also add to his art collection. 'I love collecting, I probably have the biggest collection of wood engravings in the country, but I impose the same cash limit on all my purchases.' What is that, I wondered, bearing in mind the often ludicrous prices of the art market. ' pounds 50,' he replied. 'Has been for some years.'
The arts world can take note. This man has a real interest. But he's no big spender.
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