He nearly quit acting in the 90s, but now Irrfan Khan is one of the most wanted stars in India and Hollywood, with roles in Slumdog Millionaire and Life of Pi

Character actors, we are routinely told, are usually the sort with "interesting" looks. The kind directors wouldn't hang a blockbuster on the cheekbones of, but would, say, use for depth, flavour, grit – every creative euphemism that conveys "solid acting, shame about the face". At 48, Irrfan Khan is a character-acting veteran. Considered too "unconventional-looking" for Bollywood leads and, too little-known and Indian for Hollywood's, Khan has perfected the art of being that guy, from that thing. Since his breakthrough in Asif Kapadia's The Warrior in 2001, right up to Ang Lee's award-magnet Life of Pi just over a decade later, Khan has built up the steady level of kudos that comes from being a serious, dependable actor.

It's a shock, then, when he emerges from the hotel lift, the elevator ping cheesily announcing his megawatt smile. Khan is, in fact, Blue Steel good-looking. True, he's just swallowed up half of our allotted interview time to be preened by hair and makeup, but he is head-turningly handsome: tall, lean, raffish, chiselled. In the flesh, there's none of the world-weariness characterised in the dozen or so cops he's played on the screen, or the creepy intensity that makes him a great Bollywood villain. The second surprise is that he's funny – in a dry, deadpan way that is all about the delivery.

"You're an entertainment writer, then?" he says by way of introductory small talk. "It's culture, really," comes my prissy mumble. "Ah, yes, culture. Hmm. Which isn't entertaining at all, is it?" And we're off. Once inside Benihana's, a heritage sushi chain briefly fashionable sometime in the mid-60s, Khan makes polite chit-chat about the London Indian film festival and why he's keen to promote it (although, curiously, there is no major screening of his new film, D-Day, within it). He is here for the season's flagship event: a masterclass at the BFI with Asif Kapadia, the director Khan gratefully credits for saving his career when, in the late 90s, he was considering quitting.

Khan in Slumdog Millionaire. Photograph: FoxSearch/Everett/Rex Featrues

"I came into this industry to tell stories and do cinema and I was stuck in television." Which, on the Zee and Star Plus networks in South Asia, meant soap operas "chasing middle-class housewives and the [poor and illiterate]. Once, they didn't even pay me because they thought my acting was so bad." Then Kapadia and The Warrior came along and Khan had suddenly bagged an acclaimed feature-film role. And a lead at that.

"Asif and I have been longing to work together again since then. I've been watching his last film [Senna]. There was a pirated DVD version in India I could have watched but I thought, 'No, I want to watch it on a proper screen.'" He builds up the importance of really saving it, to appreciate Kapadia's Bafta-winner as intended. "I did eventually see it on a screen. A kind of tiny screen." Where? "Oh, on an airplane." And there's the humour, teasing throughout the edges of our chat.

Khan was born to Muslim parents in the Jaipur village of Tonk. His mother's side has royal lineage and his father's side was well-to-do, but Khan Sr was a self-made man. "He had a tyre shop but, really, he was a hunter." Khan, the eldest of two brothers and one sister, side-stepped the family business when his father died and escaped to drama school. "First, I pursued cricket, then I tried business, but I quickly got bored. Cut, cut, cut to drama school. No one could have imagined I would be an actor, I was so shy. So thin. But the desire was so intense, I thought I'd suffocate if I didn't get admission."

Three decades later and he is no less passionate. Danny Boyle described his performance in Slumdog Millionaire as "beautiful to watch", and the late Roger Ebert commended him for subtle, engrossing work in Mira Nair's The Namesake. Mostly, though, Khan morphs on screen. He seems to disappear into the role, his face almost unrecognisable from one picture to the next: getting older and then younger-looking – blandly indistinctive at one turn, with sharp, penetrating features the next.

Given his reputation for integrity, for being all about the craft (and he talks, at length, in those terms), it almost seems churlish to ask him about vanity and whether he's had work done. Almost. "I've never looked to create an image where people fall in love with my face or style. It does cross my mind. But I've been trying to create a space for myself where I don't depend on that." He is similarly vague about the beauty ideal in Bollywood – where he is arguably boxed into particular roles because the predominant aesthetic of the past two decades has been body buffed, skin-bleached. Even once-darker megastars – Shah Rukh Khan, Deepika Padukone, Preity Zinta – have endorsed "skin-whitening" products. As a darker, slighter actor, is there pressure to conform to the industry ideal?

Khan in the Amazing Spider-Man. Photograph: Alamy

"I did try to do it but it made me feel empty. I cannot do things which don't come naturally to me. Initially, I did try everything. But you have to stick to your convictions and stand by your plus points. [Going to the gym] is not exciting for me. I want to connect with a story and hit [audiences] in the heart with a different way."

It's perhaps this attitude and a distinct lack of baggage – "I don't have an image to protect" – that explains why he, rather than much bigger domestic stars including Anil Kapoor or Amitabh Bachchan, has cracked both domestic and international markets. In the west, he has become the go-to Indian, bit-parting his way through Darjeeling Limited, A Mighty Heart, HBO series In Treatment and The Amazing Spider-Man. Meanwhile, Mira Nair has made him something of a muse: she was the first to spot his talent and plucked him from the National School of Drama (NSD) in Delhi for Salaam Bombay in 1988. Khan's part ended up on the cutting-room floor but the pair reunited on The Namesake in 2006 and for Nair's segment in New York, I Love You. In Bollywood, his career has stealthily progressed over dozens of films.

"I always object to the word Bollywood," he explains, delicately picking over his sushi. "I don't think it's fair to have that name. Because that industry has its own technique, its own way of making films that has nothing to do with aping Hollywood. It originates in Parsi theatre." So what defines Indian cinema? "Celebration, [we] celebrate everything and Indian cinema is an extension of that, so why did they lose their identity by calling it Bollywood?"

What about the indie Indian cinema scene – the "Hindies"? The sorts of films programmed in the London Indian film festival are feted and gaining traction with the South Asian diaspora in recent years, but how do they play at home? "They are doing great! That's why the industry is changing, because those films are bringing in money and they can't ignore it. Everybody's watching them." Admirably, Khan and his wife, writer Sutapa Sikdar, whom he first met in his NSD days, are setting up a production company to support the films he says are bringing back the creative spirit and experimentation of India's once-burgeoning parallel cinema movement.

"I wouldn't call [the Hindie films] arthouse but they do have a more original voice. You still have to entertain [Indian audiences], you cannot make them think. Or, you cannot leave them thinking. If you leave them thinking, you have to give them catharsis." I warn him this could sound grotesquely patronising in print. "But that is the way it is in India, they want an emotional connection. If you see a dark film that disturbs you, India won't take it. If it is tragedy, they will love it. They love to cry. That's for me, also. The first thing I do when I read a script is to find what hits me emotionally. That's what I connect to."

His harshest critics, he says, are his two sons. Not quite teenagers yet, but savvy enough to be telling him "what works and doesn't work for them. There is no bias. And they're my sons." His mother is proud, though he suspects she'd be happier if he gave it all up and became a teacher in his home town, as he once promised. "My mum is a conventional Muslim. Things I have learned from Islam are fantastic and I will carry them all my life but I am more open. I feel healthier that way." All in all, he seems pretty happy with his lot. Content and relaxed in a way that doesn't often come across with actors, no matter how successful. "Yes! I don't know why I get such cynical headlines. They always make me sound like I'm suffering from life." A car arrives to whisk him to the BBC and our 30-minute lunch is up. Khan puts his sunglasses on and taps out a cigarette. "I have lost the temptation for things that come through stardom. One day I'd like to enjoy my life without fame. Now ... I enjoy it, you know?"