It’s impossible to spend an hour in James McAvoy’s company without being humbled by his brain. The young Scot has recently enjoyed a sensational run of parts in gritty television dramas such as State of Play and Shameless (in which he met and later married his screen lover, Anne-Marie Duff). But it’s the intelligent performances he has banked on film that mark him out as one of the most exciting natural talents I’ve seen.

The 27-year-old actor is handsome enough in a badly-drawn-boy sort of way. The face is neatly chiselled, and there isn’t much meat on his bones. But the Glasgow accent is raw and scruffy, as is the charm, and the outfit — a rumpled black sweater and jeans.

In the past couple of years, McAvoy’s uncanny versatility in front of a camera has won him an enviable spread of roles, notably that of the slippery Mr Tumnus in The Chronicles of Narnia, and a seat on the Bristol University Challenge team in Tom Vaughan’s geeky comedy Starter for Ten. But it’s the rash of quality films McAvoy is about to star in this year that reveals just how fast and furiously this actor is coming, and the cut-throat competition that exists for his signature.

For the record, there is Joe Wright’s eagerly awaited adaptation of Ian McEwan’s novel Atonement, with Keira Knightley; a controversial Jane Austen biopic, Becoming Jane; a dark tango with Christina Ricci in a modern-day fable called Penelope; and the lead role in Universal Pictures’ no-expense-spared sci-fi block-buster Wanted.

But the first film on the block is Kevin Macdonald’s extraordinary account of the unlikely friendship between a naive British medic (played by McAvoy) and Idi Amin in The Last King of Scotland. It opens this week, and McAvoy is terrific as the blinkered young narrator, and conscience, of the movie. He arrives in Uganda as a humble medical volunteer just as Forest Whitaker’s feral Amin wrenches control of the country from Milton Obote.

The impressionable Dr Garrigan is unexpectedly sucked into the dark bosom of this bloody regime when the tyrant takes a wild and instant liking to him. He is plucked from his bush hospital in the middle of nowhere in the presidential limo and whisked to a compound in Kampala as Amin’s personal physician.

The film, based on Giles Foden’s “half-true” novel, sheds most of the back-story to explore the ghastly price of the doctor’s collusion.

McAvoy still seems astonishingly young to play the linchpin in this big, sexy African adventure. “Yes,” the actor agrees. “I was very worried that I was too young to begin with.” He pauses to scratch his unruly curls. “But actually I’m spookily similar to Garrigan. We’re the same script age. We grew up in the same part of Scotland. And we had comparable educations, though we are from slightly different backgrounds.”

Garrigan comes from a dour and stuffy lower-middle-class family in Foden’s book. McAvoy hails from a housing estate in west Glasgow, and studied at the Royal Scottish Academy of Music and Drama. His parents split when he was 7, but young James and his sister subsequently spent an unremarkable childhood living with their mother’s parents. If acting was something of an accident, drama school was a shock. It took him years to cope with the endemic insecurity of his vocation, even when the awards started rolling in.

“I’ve been doing this job for seven years now, so I’ve got a healthy level of wariness about the industry.

“Success for me has always been defined by employment,” McAvoy muses. “I don’t like hype. I don’t like the free stuff people try and give you. I don’t really like parties. And I don’t know why.”

Is it something to do with his background? “It might be. But I think it’s just the fact that I’ve learnt my craft the hard way. If I was suddenly crowned a major movie star at 21, which is what happened to Keira Knightley and Orlando Bloom, I don’t think I could cope. I feel sorry for those guys, because they’ve had no time to build any experience or skills. You suddenly just have to be good. You also have no training in how to deal with what you have become.

I’ve got to where I am very, very slowly. If I fell for the hype now I’d feel I’d be devaluing all the work I’ve done when I had little choice over scripts. I’ve been lucky in that I’ve always managed to find parts that pushed me.”

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