He left at midnight. Nine hours later he is back, having made the short journey from his home to his office, a converted chapel in Hampstead. Here he works on Cold Mountain with Walter Murch, editor of The Godfather, and can barely keep his hands off the movie or resist showing it to me. “Come on, choose your favourite scene from the book,” he says, for Cold Mountain is based on Charles Frazier’s bestseller about a Confederate soldier’s Ulysses-like return home from battle. The one where the bear goes over the cliff, I suggest. “Not in it. Was in one draft, but it went. Sorry. Another.” OK. The bit where the old woman tells Inman, the hero, that marrying a woman for her beauty makes no more sense than eating a bird for its singing.

“Er, that’s gone too.” Instead he shows me his own selection, something from the beginning (a Dante-esque battle scene involving 1,200 extras), then a massacre from the middle (Straw Dogs-like in its cruelty), and his ending where Inman, having made it back to Cold Mountain, still manages to get himself killed. On the screen, as an emaciated Jude Law lies dying, an improbably radiant Nicole Kidman, playing his girlfriend, kisses him passionately on the lips, as if love might resuscitate him.

Anything more than screen chemistry going on there, I ask, having read the tabloids. “Absolutely not,” says Minghella sternly. “Such nonsense. They hardly had any scenes together.”

The movie will be released on Christmas Day in America. All I want, I say sincerely, is for it to be a Saturday afternoon in January and to be watching it. He agrees. This is a Saturday afternoon movie, one to lose yourself in and leave the cinema surprised it has turned dark.

Director of the Oscar-garlanded The English Patient and the slightly less ecstatically received The Talented Mr Ripley, Minghella is Britain’s king of highbrow box office. But as the new chairman of the British Film Institute his job is also to promote the different kinds of films it exists to preserve and promulgate: art-house movies, shorts, documentaries, foreign-language films. Fortunately, the steel canisters in the BFI’s vault house the same celluloid that furnishes the mind of the British blockbuster-maker and Portsmouth FC supporter. “The simple answer to the question ‘what films do I love?’ is that the movies I love tend to have been made in a foreign land or before 2003,” he says.

Luchino Visconti’s The Leopard (1963) which the BFI is currently distributing, would be an example. It is better, possibly, than any of the films showing at your nearest multiplex, but marketing persuades us that those are all the choice there is. He is pleased that in the week of The Leopard’s rerelease it was among the top three earners in terms of attendances per screen, but he knows that many people will have stayed away because they feared it would be a slog.

He doesn’t spell this out. He doesn’t need to, but the BFI’s worthy reputation is partly to blame. “The BFI,” he says, “is a typical British institution in that it doesn’t sing its own praises and has, perhaps, been guilty of modesty or of not understanding sufficiently how to reach out so people know how to use it. It can borrow some Hollywood skills in terms of advocacy. How do you let people know there is a marvellous film showing at the NFT that it is not spinach, not ‘good for you’; just good, exciting and entertaining?” Since every film he has made has been produced against the odds — Fox pulled out of The English Patient shortly before filming began — he knows something about overcoming resistance. “I am as determined to overcome the resistance that The Leopard might be ‘medicinal’ as I am to that being thought about my own work.”

One tactic will be to broaden this autumn’s London Film Festival, which the BFI runs. He is delighted that The Times is the new principal sponsor because The Times is a national paper and he wants a festival that will show films and hold events all over Britain.

Once again, besides its “interpretative, contextualising and celebratory” functions, it will show films that others would not risk showing. This time, you will not need to be in London to see them. He sounds excited, but even his enthusiasm cannot make the BFI anything less than a slightly dispiriting topic. It gets a £14.5 million public grant and people wonder where it goes.

The NFT on the South Bank in London undoubtedly subsidises many a happy evening for cinéastes, but for the rest of us its dingy solemnity is off-putting: the grim monthly pamphlet advertising its programmes, the walk there past its long-closed Museum of the Moving Image with its rusting Daleks, and of the closure of the NFT film bookshop. I protest, particularly, at the Imax cinema at Waterloo, where 3-D dinosaur films seem in permanent repertory. Why on earth is it run by the BFI? There is a long pause. “Well, the IMAX breaks even. I think the money is being spent well. Please don’t ask me about IMAX because then you just run into my views about cinema.”

But he is the chairman, isn’t he paid to have views? “I am not paid anything. Look here’s the thing and I wish your tape recorder wasn’t on. I don’t want to be rhetorical. I have tried to meet everyone who works for the BFI and find out what they do. Until I know more it is wrong of me to judge too much. I mean, when you get individuals from the BFI in a room talking it is exciting. It is just exciting in too quiet a way.”

The Times photographer’s complaint is the reverse, that Minghella is so noisily talkative that it is hard catching his face in repose. When it comes to the BFI, however, considered silence prefaces the chairman’s almost every reply.

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