Michael Gambon once claimed that he used to be gay. He had to give it up, he said, because it made his eyes water. He told another interviewer he'd started his career as a dancer in the Royal Ballet. He had to give that up as well, after he fell off the stage.

'It's in one of those handbooks,' he tells me. '"Used to be a dancer." The reporter said to me, "Ooh, was it painful?" So I said, "Yes, I fell through the timpani."'

You will gather that Sir Michael Gambon is not invariably and entirely truthful. Making Sleepy Hollow with Christina Ricci, he used to tell her elaborate stories about the clubs he'd been to the night before and the drugs he'd taken. 'Oh, yes,' he says fondly. 'I used to tell her terrible fibs.' Ricci thought it was a hoot. But it can also be a bit embarrassing if you're the hapless reporter who notes down 'fell through timpani'. So when his first words to me are, 'I had a car crash last night,' I am inclined to ignore him. I ask him instead about the play he is currently rehearsing, and only after about 10 minutes realise he really did have a car crash last night.

A big, bear-like man, Gambon slumps behind a cloud of cigarette smoke in the corner of a sofa in rehearsal rooms near Waterloo. His grizzled hair is long and his face is battered, baggy and jowly. He's wearing a scruffy suit, conveying a sense, overall, of someone a bit seedy, dissolute, tramp-like. But he's rehearsing Beckett's Endgame, in which he plays a man who is blind, in a wheelchair and dying, and whose parents live without legs in their own excrement in dustbins, so I assume it's just a matter of getting into the part (and is not the impression he seeks to convey, for instance, behind the wheel of his red Ferrari, his car 'for posing around London'). His cheeks are livid with bruises, although these turn out to be the result, not of the accident, but of dental treatment. He has, he tells me proudly, in the slightly slurry, old-drunk voice the treatment has temporarily given him, eight titanium plugs in his gums.

He was actually unhurt in the crash, which was the fault of the weather and only damaged the car. 'I'm not thinking about it,' he says. (Now, this, clearly, is a lie.) 'There's no point in losing sleep over it. It's a year old. Positive thinking.'

I am actually less worried that Gambon will tell me lies than that he won't tell me anything at all. He is notoriously publicity-shy, rarely gives interviews and, when he does, works hard not to give anything away. He is sometimes described as having a wife, or an ex-wife (Ann, or Anne, Miller), occasionally a girlfriend. At some point he seems to have lived in Kent, but probably doesn't now.

'Paul Schofield said something like, "If I'm not acting in a play, I don't really exist,"' he announces quite early on in our conversation. 'Those weren't the exact words, but he meant it's only when I'm acting in a play that I've got something to say about the world. And then why should I talk, when people can come to see it?'

Acting, for him, is a kind of compulsion - 'overwhelming, like being a priest. Something you want to do. Nothing to do with being well known or anything. That other thing comes as an unfortunate part of it. And it's loathsome, the whole panoply of it. I've always tried to be an actor who... I just plod on and try to keep my mouth shut, mind my own business. I find the whole thing about people's lives... I can't understand it. I'm always astonished that people want to know anything about me.'

'But aren't you interested in -' (I snatch at a name, forgetting he had a scene in her recently released movie, Sylvia) 'Gwyneth Paltrow, or whoever?'

'I did another film with Gwyneth,' he says. 'I'm more interested in my dentist.'

Gambon seems to guard his privacy as assiduously in private as he does in public. 'He restores antique guns and tells jokes that can go on for days,' says Alan Ayckbourn. 'I don't know any more about him than that. He's only really public on stage.' Matthew Warchus, who is directing him in Endgame and has worked with him twice before, says, 'He's very private. I know other actors who are like that and it's connected to the acting. In the theatre, among actors, directors, writers, the skill - talent - is a by-product of social dysfunction: outsiders, shy people. Many actors are incredibly shy. They're channelling something that would otherwise be extremely problematic.'

Gambon, whose job is to abnegate himself, presumably can't see why a person who subsumes himself in other characters should be interesting. The trouble with this, though, as Matthew Warchus suggests, is that actors are in the business of channelling emotion; not primarily learning and expertise (as in the case of his dentist) but feeling.

'He's eminently readable on stage,' says Ayckbourn, who has directed him several times. 'You can see into his heart.' And people are understandably curious about where that comes from. 'I know when an actors is full up with something,' says Warchus. 'And it might well be to do with pain from their own lives, or scar tissue from traumatic events.'

Gambon, as he acknowledges, is an instinctive, rather than a technical actor: 'I admire technical facility in others, but I'm a hit-and-miss merchant. I'm afraid I do my own sort of thing.' His own sort of thing is incredibly powerful: he has the ability to express subtlety and intensity of feeling through apparently small movements or vocal inflections. He does it while he's talking to me, explaining the central character in The Caretaker. 'Someone says to him, "You're Welsh, aren't you?" And he says, "I don't know. It's hard to cast your mind back."' And as he speaks the line, something about him goes limp and defeated, and there is a sense of pathos, loss, and longing. It's like getting a sideswipe; it knocks the breath out of you.

Ayckbourn experienced something similar when he was directing him as Eddie Carbone in Arthur Miller's A View from the Bridge. 'He can be immensely emotional. If he decides to go for something, it is quite awe-inspiring. The day he stood in the rehearsal room and just burst into tears as Eddie - no turning upstage, no hands in front of his face - just stood there and wept like a child, was heartbreaking. And he does angry very well, too. That can be scary.'

With such access to emotion and such facility in its expression, Gambon's reluctance to talk about his personal life is understandable; he could get himself into all sorts of trouble. Besides, he works at sounding the right emotional note. He must fear that anything he might say in an interview would sound, to his perfect emotional pitch, luvvieish or faked, trivial or overegged.

Michael Gambon was born in Dublin in 1940, but moved to London as a young child. He grew up in a mostly struggling Irish immigrant community in Mornington Crescent, attended St Aloysius Boys' School in Somers Town and, briefly, another school in Kent, before leaving at 15 to become an apprentice toolmaker at Vickers Armstrong in Crayford. He completed the apprenticeship and he remains fascinated by mechanical things. He collects antique guns - and now has around 800.

'I belong to quite a lot of learned societies. We collect firearms and discuss them at dinners and clubs and things' - old clocks, and watches. He has a pilot's licence and, as well as the Ferrari, he tells me vaguely, 'I've got a Mercedes, BMWs and all that shit.' I wonder whether he could have been a happy engineer had he stayed at Vickers, and he says, 'No, I'm a malcontent. I would want to be an actor.' So is he also a malcontent actor? 'Yeah. I think you have to be, don't you? To get going.'

He didn't go to the theatre until he was 19, but he loved the cinema and had a sense of acting as 'like a heartbeat, something inside me. Some dream. I think it's being a dreamer as a child. Dreamy kids become actors, don't they?'

He did some amateur acting, then got his first professional job on the basis of a largely confected CV that he sent to the Gate Theatre, Dublin. His first big break came when he joined Laurence Olivier's startup National Theatre in 1963, as 'one of his spear-carrying boys'.

He was never a matinee idol ('No, I like being rough round the edges. A big, interesting old bugger'), though he was once taken to an office in Mayfair to meet Cubby and Albert Broccoli. 'I was given a smoked-salmon sandwich and a glass of champagne and Cubby said, "We're looking for a new James Bond," and I started laughing. I said, "James Bond, me?" [He sounds, at this point, exactly like Tommy Cooper.] "I'm not the right shape." He said, "Well, we have ice bags for Sean's chest and that thing there [Gambon points to his jowls] that doesn't take more than two days and the recovery period's a week. Teeth, well we can do that in an afternoon. And Sean wears a piece." I said, "I know that." He said, "I'll get a toupe for you."'

In the end, nothing came of it. We should be grateful: instead of a plasticised Bond, we have had a succession of characters who have been knocked about by life, who are grandly individual, who are by turns enraged and vulnerable. The roles he is most likely to be remembered for are the ones he instantly mentions as his own favourites: Brecht's Galileo at the National in 1980, The Singing Detective on television in 1986, and Eddie Carbone at the National in 1987. He is, as Ayckbourn points out, particularly good at playing 'simple' characters such as Carbone - not least, perhaps, because he can find their complexity. 'We're all deeply complex, aren't we?' he says to me. 'We're all that much,' he holds his hands close together, 'on the surface and that much,' he moves them wide apart, 'beneath: the subtext of life. And that's the acting. The subliminal surface there and the vast, vast chasm of everything - bringing some of that to the surface, suggesting it.'

Matthew Warchus says: 'Part of what you're doing in rehearsal is building the only partially visible and the invisible. A great performance gives a glimpse of something, so that you feel there's a huge story behind the character. And there's an enormous story behind Michael. But I think there's a secret part of actors that it's best to leave secret.'

Last year, Gambon was cast as Richard Harris's replacement as Albus Dumbledore in the third Harry Potter movie. I ask if he was conscious that he was taking over a much-loved character, and he seems mildly affronted. 'Do a sort of Richard Harris impersonation, you mean? It never crossed my mind. If you were playing Lear, you wouldn't copy the last person to do it.' While Harry Potter was in production, he also managed to fit in the making of six other movies: 'Sylvia, a gangster film called Layer Cake, another one called Being Julia, with Annette Bening, one in Canada with Kevin Costner and one in Italy with Bill Murray, called The Life Aquatic. It's really about Jacques Cousteau - a comedy, directed by Wes Anderson.'

At this rate of movie making, he can afford the hobbies. A duelling pistol, he explains, might cost £8,000, while 'a beautiful inlaid German wheel lock' might go for £28,000. He also has a nicely lucrative career in advertising, making the most of a voice so gurgling with richness that it sounds oiled - and which is capable of sounding self-consciously posh, like Captain Mainwaring in Dad's Army, and of skidding erratically over the vowels.

'I'm an anorak,' he says with some satisfaction. 'I've always been an obsessive collector of things. Richard Briers collects stamps. I collect cars and guns, which are much more expensive, and much more difficult to store.'

So where is the house you keep them in? I inquire innocently. 'Greater London', he answers, coming over all curmudgeonly. And he won't tell me if he's married: 'I don't talk about it.'

Lee Evans, who is playing his servant in Endgame, and with whom he evidently has a very good relationship, claims he doesn't know either. 'I wouldn't really like to ask. I can't work him out. I know he fiddles around with cars at the weekend. He's all over the place. That's the most fascinating thing about him.'

Some reports say that you're married, some that you aren't, I persist pointlessly. He pretends to guffaw. 'It's good, isn't it?' But he perks up when we get on to cars. 'They named a corner after me on Top Gear, Gambon Corner. The last corner on the circuit.' (He's talking about the track around which celebrities drive so that they may be ranked for speed.) 'I almost killed myself. I had four wheels off the ground. I'm the oldest person ever to have done it. It was raining and I did very badly. I was so bad that the BBC made an edict after that - you must get a roll bar, because that bloke could have killed himself. So Jeremy had to get a roll bar fitted in that Japanese piece of shit they drive around. Jeremy had a Ferrari, too, but he's sold his now. He's got an SL 55 AMG.'

So, he's a bloke. But a sensitive one. Lee Evans describes him as 'patient and modest' and Warchus as 'amazingly gentle. Very masculine, but very kind.'

He has never wanted to direct. 'I'm too subversive. I like being with actors and knocking the director. Lee and I are in this play with Matthew, whom we love, and we come out here and talk about him. There's a them-and-us thing. I wouldn't want to do it. I'm not confident enough.

'I'm always the bloke just behind, hiding, and when you see the opportunity, shoot out, grab it, and hide again. In an army I wouldn't be an officer. I'd be a sergeant or a corporal or something.'

He's known for subversive fooling around - for ad-libbing upstage, or moving a pencil a couple of inches across a table after a director has set up a shot. 'He's a clown,' says Warchus. 'He has the gravitas, and sadness, and extraordinary comic nature of a great clown. And he's also great fun and remarkably easy to work with.'

In the end, what makes Gambon a great actor is his willingness to take risks. 'He tends to make unusual choices,' says Ayckbourn. 'He rarely does what anyone else would do.' In a recent 'not terribly happy' production of The Caretaker, he tried a different accent in each scene. It didn't come off, but he says he doesn't regret it. 'I live in fear of being a contented passenger. I'd rather get parts I can't play.' There is a sense, as a result, when he's on stage that what's going on isn't entirely under his control. And probably he's right in his assumption that to be this adventurous, he needs to be unknown, capable of being protean, for the audience to have no stake in his being a certain kind of person. Besides, he is acutely aware of himself as a performer, and I suspect it seems somehow to him both self-aggrandising and humiliating to be required to mount a performance about himself.

He's too busy worrying, anyway. 'I want to be good all the time, so I feel anxious. But if you weren't like that, you'd be dead, wouldn't you? If you went out happy down the road, la la la. I've never been like that. I don't want to be.'

'Hmmn,' I say, not entirely understanding. 'You need to feel edgy?'

'Yeah.' His eyes are hooded behind the cloud of smoke. 'I talk a lot of shit, don't I?'

· Endgame is at the Albery Theatre, London (0870 060 6621)