Mark Strong looks at me with distaste. “I can’t stress enough how totally uninterested I am,” he says. Fortunately, he is talking about fame. “There is no part of me that wants to have to pull the blinds down when I’m talking to my wife about dinner because some photographer is in a bush outside.”

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One of Britain’s most respected character actors – and perhaps its very busiest – he’s aware of the irony in criticising celebrity while giving an interview. He does them, he says, only when he has made a film he believes in.

He has two such movies coming out, thriller Before I Go to Sleep (in cinemas from Friday 5 September) with Nicole Kidman and Colin Firth and The Imitation Game (opening in November), a portrait of wartime codebreaker Alan Turing. Strong will be Stewart Menzies, head of MI6; Turing is played by Benedict Cumberbatch.

Given his aversion to fame, Strong can only sympathise. “It’s awful, because everyone wants a picture for Facebook, and if you’re Benedict you now can’t walk down the street. I wouldn’t wish it on my worst enemy, and I think he’s lovely.”

Strong met Cumberbatch on the 2002 TV drama Fields of Gold where he also met his wife, producer Liza Marshall. “It was Benedict’s first job. Tiny part. He was a guy being told to get out of a toilet. I remember being by the bar at the wrap party and wishing him good luck.” Before I Go to Sleep (left, also produced by Marshall) is a twisting tale where Strong’s Before I Go to Sleep (left, also produced by Marshall) is a twisting tale where Strong’s villainous image sits front and centre, echoing his icy stillness in Kick-Ass, Guy Ritchie’s Sherlock Holmes and Tinker Tailor Soldier Spy.

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“Well, heroes don’t get the outrageous costume or the fantastic one-liner. And I find villains interesting because they’re exotic. I don’t actually go home and menace the neighbours.”

Sipping bottled water in a crisp blue shirt, he looks a figure of gleaming health at 51, amiable and dry with a certain steel beneath. He could be any professional family man who gets to Arsenal games when he can and moans at his two young sons to tidy their room, “so that in 20 years I’ll have spared two women being stuck with guys who can’t pick their pants up”.

His own father was Italian and his mother Austrian. They met when she came to London at 18, in the early 1960s, but soon afterwards dad disappeared and mum raised him alone – changing his name from Marco Salussolia so he might be more easily accepted in England.

“As an only child, particularly if you’re a boy without a father, you have to work out for yourself who you’re going to be. And I do think, over the years, I’ve developed a need for control.”

He has no PA. He says he would spend all day checking up on them. He also loathes being “infantilised” on movie sets. “An assistant director said to me the other day, ‘Where are you going?’ I said: ‘Across the road.’ And she said, ‘Wait, I’ll get someone to take you.’ And I had to remind this 12-year-old, I actually cross the road on my own most days.” He grins, though with limited amusement. “And they all have walkie-talkies so you hear them muttering: ‘Mark is now walking to the set. Mark is now going to the toilet.’” He shakes his head. “I have literally had to tell people to stop putting my socks on for me.”

As a young man, Strong might have been lost to Britain. At 18, he arrived at university in Munich, to become a lawyer, “complete with BMW and raincoat”. Once the reality of German legal textbooks sank in, he sped back to London. The taste for performance he had stumbled on in teenage punk bands evolved into studying drama, and from there into a theatre career.

On TV, he graduated from The Bill through Prime Suspect, on to the award-winning 1996 drama Our Friends in the North. But among a cast that included Daniel Craig and Christopher Eccleston, he seems to have been left behind.“I was sharing a flat with Danny, and he didn’t work for months afterwards, whereas I went straight back into a play. So I’m making £300 a week, thinking, ‘Poor old Danny.’ ”

Though his co-stars have variously played Sherlock Holmes (Cumberbatch), James Bond (Craig) and Doctor Who (Eccleston), there is no hint of envy. Still, desperate to get into movies, he took the decision to stop doing TV because, “with films, you have to be available”.

I ask what advice he might give a young actor facing the same dilemma and for once, he looks flustered. “I can’t imagine I’m that guy now.” Why not? “Because I don’t feel experienced enough.” He half beams, half grimaces. “And frankly, I don’t feel old enough, either.”

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Before I Go to Sleep is out in UK cinemas today

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