'Maybe I want to pack acting in," says Tom Wilkinson, one of Britain's best-loved actors, in an endearingly rumpled voice. Why would you do that? You've been nominated for Oscars and you're about to fly off to start filming The Lone Ranger with Johnny Depp. Acting seems to be working out pretty well for you.

"Oh, I don't know," he replies, as casually as if he's just commented on the weather, as opposed to telling a journalist something that would give his agent a fit. "I haven't really thought about it in any coherent sense. I'm not a good traveller. I never used to mind all the time away from home, the hanging around, but now I think, 'Oh, what time is it? Come on!'" He ponders for a minute then says: "No, I can't quit. What would I do? Maybe I should just make movies in Muswell Hill, then I could go home for lunch. That would be good."

But the movie you're making with Depp is in New Mexico, right? "Oh, don't start!"

As well as the travelling, Wilkinson also finds doing publicity wearisome. Although he has been nominated for a best supporting actor Oscar twice (for In the Bedroom and Michael Clayton), been in some of the best small films (The Full Monty), the biggest blockbusters (Mission: Impossible 3, Batman Begins) and the finest TV serials of recent years (Martin Chuzzlewit, John Adams), the film that best demonstrates the nature of both his career and his personality is a clip that can be found on YouTube. It dates from 2009, right after Wilkinson won the Golden Globe for his performance in the US miniseries John Adams. He is shunted out before a press battalion looking more like a professor than a lauded actor, with his skew-whiff spectacles and disobedient hair. He stands there, waiting for a question. Eventually, after several painful moments of silence, one comes. "Congratulations," says a journalist. "Can you tell me what the real Tom Cruise is like?" Wilkinson stares at the questioner. "He's very charming," he deadpans.

"That was a pity question!" cries Wilkinson. "I was taken out there and someone said, 'Tom Wilkinson, best supporting actor for a miniseries', which is fucking meaningless, of course. And then – absolutely nothing! So that guy asked his pity question. But I didn't care." I hope it didn't ruin your mood. Winning a Golden Globe is a big deal. Wilkinson looks up with an expression that suggests boredom with awards, and surprise that his should be a source of pride. "Is it? I don't know."

Wilkinson is not your typical actor interviewee. For a start, today he seems far more interested in talking about the interviewer than about himself, kicking off proceedings with the announcement that he heartily agrees with an article I recently wrote vilifying jeans. "All that clinging to your youth," he says. "It's no good for me!" Wilkinson's Eeyore tendencies, his innate groundedness (which he puts down to his northern upbringing), and his complete disinterest in toeing the PR line reflect someone delightfully unaffected by success: it's like talking to an enjoyably grumpy neighbour, rather than someone who is – albeit reluctantly – about to make a big-budget film with Depp. As his agent Lou Coulson once said: "He's ambitious, but it's not an ambition for fame. He wants to be in line for good scripts."

"That's true," Wilkinson says. "The fame aspect has never interested me. I can see it in other actors who love being famous. Me, I don't care for it at all. If I can sidestep doing publicity, I will."

So you won't be appearing on Jonathan Ross any time soon? "Oh don't! I happened to catch a few minutes of that the other night – and it was horrible! He had David Beckham on the sofa and it was just awful. Trying to be sort of … matey," he says, spitting the word out. "Beckham handled it very well, not being drawn into this, 'Tell us how big your dick is, David?' But it makes you go, 'Shut up!'"

Unfortunately for Wilkinson (but fortunately for me), he wasn't able to sidestep the publicity for his latest film, The Best Exotic Marigold Hotel. A larky yet dark soap about a group of pensioners relocating to India, the film features a slew of British actors routinely described as national treasures: Bill Nighy, Judi Dench, Maggie Smith. While it may not be Wilkinson's finest film, he is marvellous in it, playing an elderly gay man looking for a lost childhood love. Needless to say, Wilkinson did not particularly enjoy the exotic shoot. "I never got over the trauma of being in India, really," he says.

At times, the film's Indian characters, particularly Dev Patel's portrayal of a hotel owner, veer uncomfortably close to Indian stereotype, a point Wilkinson partially concedes. "I think some people will take severe, or some, exception to the way India could be seen, the treatment of some of the Indian characters."

But what do you think? "What do I think? Hmm. What do I think?" He ponders. "I'm going to have to say that I think it pulls it off. It's meant to be a comedy, after all."

Another problem is that the group are supposed to have travelled to India as part of a holiday for the elderly, yet Wilkinson is only 64 and Nighy 62. Diana Hardcastle, Wilkinson's wife, appears in the movie, too, looking downright youthful. Wasn't he a little insulted by all this "elderly" talk? "I did feel that, but there is a convention that once you get past 60 you're in elderly territory. Maybe that's a weakness of the film, that you don't quite buy the premise, maybe that's true."

The subject of ageism really gets him going. He talks, with passion, about the injustice of Marks & Spencer staff trying to help him pack his groceries. "Well, I bristle! Do they think I'm incapable? They say, 'We ask everyone.' But I say, 'Well, you didn't do it with that woman over there!'"

Wilkinson was born in Leeds into what he describes as a family of "northern farmers". After studying at the University of Kent, he went to Rada and spent the next few years working in TV and theatre. It was on a TV job that he met Hardcastle. "It was a not very good TV series called First Among Equals, a Jeffrey Archer adaptation. It was not," he repeats, in case the point was lost, "very good." Well, you got something good out of it. "Yes, that's true."

After his fantastic performance as Mr Pecksniff in the BBC's 1994 Martin Chuzzlewit ("Yes, I was good in that. I was good!") he crossed over to film and came to prominence as an unemployed factory boss in The Full Monty. Wilkinson has played so many different characters – from enjoyably cheesy villains in blockbusters to historical figures, not to mention his extraordinary turn as an American factory worker who decides to have a sex change in 2003's Normal – that it would be reductive to say he is known for any one type of performance. But his delicate portrayals of grief and shame in The Best Exotic Marigold Hotel, In the Bedroom and even The Full Monty are particularly fine.

"When I read a script I want to do," he says, "there is an act of recognition, one of, 'I can do this – in fact, I can do this better than anyone in the world.'" The thought makes him look almost content, but then the clouds encroach again. "That doesn't happen with every job. The job I'm about to do doesn't have that 'I can do this' element."

Still, at the next awards show, it will give journalists something to ask you about. "Yes! I'll be asked what it was like working with Johnny Depp. And I'll say, 'It's OK.'"