Broadbent plays the heroine's dad, a decent chap adored by his chaotic daughter and momentarily abandoned by a wife enamoured of a shopping-channel love god. It is a small part, but the image of him sitting in his crumpled pyjamas as Christmas jingles on without him is more poignant than any of Bridget's romantic miseries. "I just played him pretty straight," says the actor, as if that were a huge relief. You can see why it might be so.

Broadbent's specialism has become mildly eccentric characters with theatrical occupations and manners to match - characters such as WS Gilbert in Topsy-Turvy, for which he won best actor at the Venice Film Festival, or the gluttonous lothario Warner Purcell in Woody Allen's Bullets Over Broadway. His genius is needing to do very little to conjure believably comical or sad oddballs, always with that Pooterish view of their idiosyncrasies as perfectly normal, thank you.

By comparison, the real man is shy, a bit of a mumbler, prone to letting his sentences trail and die as if he never liked them much anyway, so gentle that you would not want to see him lose his temper. If you're not careful, you find you are interrupting him, and he lets you ramble on, possibly thinking you a complete fool, possibly not, while his ponderousness masks a fierce intelligence. People must have underestimated him at times; when he tells you he wrote himself off at school at an early age, you can see how that might have been allowed to happen.

Right now, Broadbent seems more in demand than he wants to be; he works constantly, unable to turn down the juicy parts he is offered. So adept is he at playing larger-than-life that Martin Scorsese cast the perfectly English actor as an infamous New York state senator, Boss Tweed, in his forthcoming Gangs of New York. Set in mid-19th-century downtown NY, it follows the corpulent, archetypally corrupt Tweed as he exploits the turf wars between Irish, Scottish and Dutch hoodlums before the Italians arrived and the director's beloved Little Italy emerged. "He was quoted in The New Yorker a month ago," says Broadbent, who researches all his roles diligently, "in an article about the presidential election, as having said, 'It's not the electorate that counts, it's the counters that count.' So that seemed pretty relevant."

Does he mind being sought out for such inevitably flamboyant performances? "Directors probably know that I'm prepared to make a fool of myself. I'll go off at the deep end - it's what they taught me at drama school: be prepared to fall flat on your face. Some people are, and some people aren't, but I think it's vital for a sustained career. You can be cool for a few years, but it gets boring. Keeping oneself entertained is the aim. I hate repeating things, and although he's larger than life, Tweed is breaking a lot of patterns for me. He's American, and at least he has nothing to do with the theatre."

But before that - with barely a gap between - he shot Baz Luhrmann's funky musical Moulin Rouge, starring Nicole Kidman, a "terrible love story" based on the myth of Orpheus. Broadbent plays Zidler, owner of the Parisian cabaret planning to stage the biggest show the world has ever seen, another megalomaniac in another film - along with Bullets, Little Voice and Topsy-Turvy - extolling the wonders of life in the theatre. "They're enjoyable things to do. You're allowed to act on a huge level. Nobody ever says, do less! In fact, Baz told me to try and make him say that, but he never spoke the words. I'm sure it's too much, totally over the top, probably the loudest suicide note in professional history!" His finest moment is singing Madonna's Like a Virgin. "My gag is that I sing like a virgin, and I dance like a farmer! Then 20 chorus boys dressed as waiters all join in." He shakes his head gently: "What an extraordinary life we lead."

Recently, that life has had its share of trials, especially eight months in Australia with Luhrmann, mostly locked in a Sydney studio with the worst recorded summer for years drizzling outside. "It just went on for ever. My wife came out for a while, but it is very disruptive to your life. When I found out I'd be working in Australia, I thought, as I've always done in the past, how exciting, but I've sort of crossed that bridge now. I don't want to do it any more." Added to that was the agony of padding, heavy wig, moustache and stuck-on whiskers, which he might have been accustomed to after Topsy-Turvy. "I had no padding in that and I grew my own whiskers," he says proudly, a man who can sprout muttonchops at will. Nor does he intend to dwell too long in the 19th century if he can help it. Mike Leigh recently gave him a book by Augustus Carr, a "1920s Diary of a Nobody genre". A Pooterish script for the future, perhaps? "No thanks. I've had enough of Victorians."

Before his return from Australia, the Gangs of New York offer had come through and, however much he wanted time with his painter wife Anastasia, he couldn't say no. "No matter how pissed off my wife was that I was going off again, she said if I turned down Scorsese she'd beat me up. So you have these dilemmas." He strokes his chin. "Though they're not really that awful, are they? Five years ago I'd have been biting their hands off, but once you've worked with Scorsese you're not going to be overawed by much. Equally awed, if you're lucky."

Jim Broadbent was born 51 years ago, the son of a conscientious objector who moved to Lincolnshire and established a pacifist community - and an adventurous theatre group featuring Shaw and Ibsen in a Nissen hut near Market Rasen. After the war the commune dispersed, but the bohemian Broadbents stayed on, one of a smattering of lefty households in the middle of Tory Lincolnshire. Four-year-old Jim's stage debut was in A Doll's House.

His father oversaw the conversion of an old chapel into a theatre, the Broadbent, which still hosts small touring shows. "I've never performed there, but I'd love to. If I had a one-man show, I'd do it there." There was never any problem with his unconventional choices. In fact, in a scene that could grace one of his collaborations with Mike Leigh, he describes his father taking him out to lunch in London when he was an art student at Hammersmith. "We sat next to these Rada students, and he just looked at me and said, 'Why don't you go to drama school?' So I did."

Broadbent's progress since leaving Lamda has been steady, starting in rep in Stoke, then joining Ken Campbell's 1977 12-hour science-fiction epic, Illuminatus, in which he played a dozen parts. "That was my showcase, my break." He did the original Our Friends in the North at the RSC and an acclaimed Government Inspector at the National. Teaming up with Patrick Barlow for the National Theatre of Brent in the early 1980s, they played two inadequates putting on The Greatest Story Ever Told in tiny spaces with no money. "It was a double act, like Laurel and Hardy deciding to put on the classics." When he decided he wanted to move to film, though terrified of the camera, Leigh cast him as Andy, the endearing optimist in Life Is Sweet, the performance that impressed Woody Allen.

He and Leigh have been close since their work in the 1970s at the Hampstead Theatre, sharing a sense of humour, a world view and an art-school background. "There's that particular attention to detail that an artist has, which Mike likes to apply to actors - it's the way I approach characters, too." Together they made Broadbent's script and one-man wonder, A Sense of History, essentially a monologue delivered by a psychotic, homicidal aristocrat. "That was a good film," he says, as if about to list its merits. "Scorsese's got a copy, and it got me a lot of jobs."

Broadbent's success has changed his life very little. "Nobody's ever offered me ridiculous amounts of money - unfortunately - so I've not had the temptation of fame." Perhaps he should ask for more? "The Scorseses know they'll get me without paying that much... But maybe there will be a time when I'll be tougher, if I get tired enough." He and Anastasia have a cottage in Lincolnshire, where they walk and he plays "extremely bad golf" with local chums. Do people point and stare? "It's funny, only Only Fools and Horses fans." He should tell them he has just worked with the world's greatest director, I tease him. "Never! I've known actors behave like that for real, and it's horrible to see."

Solid, sensible Jim seems impervious to the glamour of moving from one starry project to the next, from Nicole to Cameron Diaz, Marty to Baz. Despite his powerful inventiveness, you might be talking to any master craftsman, proud of his work but uninterested in spinning out a lifestyle from its accolades. The terror of interviewing such a reticent man, as modest in conversation as he can be ostentatious on screen, is that he might have just signed a deal to play opposite Brando, but unless you mention it first, he certainly won't assume you're interested.

If character actors are those who conceal themselves in total transformation, Broadbent is happy to carry the label - even if it makes him think of someone who twitches a lot. "I suppose that's what I am, as opposed to a personality actor or a Hollywood star." Is it unfair that such talents don't get the limelight and the lucre? "I think us lot are quite lucky in a way. You keep going, you don't age out of your range, you develop with it all. I see hair loss as opening up a whole new range of bald characters I can play."