This happy brood: How is David Morrissey coping with mass exposure?

It started with a scarecrow. The man known for brooding intelligence, onion layers of torment, charisma with an underbelly (charisma, even, with a real belly), the man known perhaps best of all for his Gordon Brown, started, age nine, in the assembly hall of St Margaret Mary's junior school, by singing "If I only had a brain". "I walked on stage on the first night," says David Morrissey, "and something went, 'click'. I couldn't play football, I certainly wasn't academic, I never had attention, and suddenly it was like people were looking at me."

They have been looking at him ever since. First, in productions at the Everyman Youth Theatre in Liverpool, and then in his first TV series, at 18, One Summer, and then at Rada, the RSC and the National, but most of all in films and on telly. They looked at him as Bradley Headstone in Our Mutual Friend, and as Christopher Finzi in Hilary and Jackie and as a Nazi in Captain Corelli's Mandolin and as a politician in State of Play, and as Colonel Brandon in Sense and Sensibility – but they often didn't remember who he was. "Would I know him?" said the girl behind the bar, when I ask for a quiet corner to do the interview. Now, there's a question. But the truth is that David Morrissey is that rare beast, "an actor's actor". He inhabits his roles so entirely, so convincingly and sometimes so hauntingly that you're left thinking about the character, and not the actor who played it.

Even so, I'm thrown by the jaunty figure – leather jacketed and slightly spiky haired – who strides in to greet me on a sunny bank-holiday evening. He has spent the Easter weekend playing with his children on the beaches of Suffolk. I have spent much of mine ensconced with him and a serial killer in a dark room. I've been watching Red Riding, the three-part David Peace drama recently shown on Channel 4, a cheery little seven-hour chunk of child abuse, torture and police corruption. Morrissey is magnificent as the compromised cop who takes the path of least resistance, and maximum personal gain, but loses his soul. Pasty-faced, heavy-set and saturnine, he spends his days hunched over smoky desks, fighting off memories and the flickerings of his conscience. Not a character, I think we can safely say, likely to foster any pleasant sexual fantasies.

Nor for that matter is Dad, the character Morrissey plays in Is Anybody There?, a new film starring Michael Caine, among a band of ageing English luminaries including Leslie Phillips and Sylvia Syms. Set in an old people's home that's also a family home, it's a touching exploration of the relationship between a young boy, seething with resentment at having to share his home, and parents, with a bunch of senile old codgers (one of them beautifully played by Caine). Morrissey is the boy's father: a hulking, sulking boor of a man, happy to leave the work, and parenting, to his wife (Anne-Marie Duff) while he ogles the 19-year old help. Like the last two episodes of Red Riding, it's set in Yorkshire in the 1980s and features some truly terrible haircuts and some truly terrible denim jackets. Once again, Morrissey manages to seem seriously unattractive. Which, I have to tell you, is quite a feat.

A character is a character, of course, and in a sense timeless, but in both cases the clothes and the haircuts feel like much more than dressing up. How far does period affect his thinking about a character? Morrissey sips his sparkling mineral water (and not, as I expect, his pint of bitter, but then we're in an airy, bleached-floorboard sort of a pub and not one full of sticky swirly carpets and mullets) and launches on a very long answer indeed. "It's right to say that a character is a character throughout the ages," he says, "but our means of communication is different, so our timescale is different, our access to news, our access to the media, our access to celebrities or each other. I think it gives us a busier way to our lives."

He continues with references to the Twitter age, to the sophistication in communication of his 14-year-old son and his friends, to his own lack of confidence with adults at the same age, and, eventually, Colonel Brandon. "You look at Brandon," he says, "and you think about all the things that Jane Austen doesn't give him, like what kind of war was he in, and what type of fighting did he do, what has he come back from, why has he got to this age and not got attached?" Indeed. I'm momentarily distracted by thoughts of the lovely, unattached Brandon, but I'm also getting a sense of the exhaustive amount of thought and detail that Morrissey brings to each part he plays. He's famous for his research. For the politician in State of Play he even shadowed Peter Mandelson. Love hath no greater sacrifice, etc. But is this all really necessary, or is it partly a kind of superstition?

"'Superstition' is an interesting word," he muses. "I have done jobs where they say, 'you can start on Monday', and that's been difficult for me. I recognise that there is a security blanket element to what I do, but I like research, I probably only use 20 to 25 per cent of it, but it just makes me prepared. But sometimes," he adds, "it can open a can of worms and you start panicking, and you just have to leap in there and do it." And what happens when your vision of the character you've built up doesn't quite correspond with the director's?

"Then," says Morrissey, "you have a row. You walk into the scene and there will be a line in it which is absolutely important to you and to him it's not, and it's like, 'just say the line and get on with it'. But you have to pick your battles. When I was younger," he adds, with engaging honesty, "I thought everyone was there for me. And I really did feel that my characterisation and the way I was working was the most important thing. And I would go to see the finished result and I would get depressed and angry because they had cut a scene or dropped a scene. But when I started directing, I suddenly gave that up. I suddenly started seeing myself as part of a process."

And what about theatre? Until he did In the Dark House, to rave reviews at the Almeida Theatre last year, Morrissey hadn't done any theatre for years. "I loved it and I felt bereft when it finished," he says. "But I'd fallen out of love with theatre because I was getting angry with the audience, with mobile phones and coughing and people talking or getting up and going to the toilet. Whereas in film you can have a laugh, you can talk, you can chat, but once you're going, it's very concentrated. But in In the Dark House," he adds, "I was never offstage. It was nearly two hours of me talking. I never had time to settle and get bored."

There is, I think, a bit of a theme emerging. The actor who once described himself in a Q-and-A session as "happy-go-lucky" (he had, he tells me, just seen the film) is clearly far from it. This is a man who takes his work very seriously indeed, one described by his oldest friend, Ian Hart, as "the hardest working man I know" and one who clearly likes to be in control. He is also a man who likes a serious challenge. If he seems to have something of a perfect life (married to the novelist Esther Freud, three gorgeous children, big house in Hampstead etc) he is also a man who grapples increasingly with the Big Issues, one even, perhaps, for whom the gathering clouds of a mid-life crisis aren't as unimaginable as they once seemed.

"When you are in your late teens or early 20s" he says "you're full of paranoia but you do have a lot of energy and you prosper. It's a brave new world and it's great. The older you get, work reflects how you feel. You start thinking about how your kids are growing up, you think about the world you are bringing them into– your mortality. All those things affect your work. You start playing characters at the age you are, so you are working through your life like a man looking back over the years and the mistakes he's made."

Morrissey, the son of a cobbler and a mother who worked for Littlewoods, was born in Everton and grew up in Kensington, a part of Liverpool that's rather less posh than its London counterpart. He's not keen on the working-class-boy-made-good label, but admits that his "very northern work ethic" comes from his background and his parents. It was from his upper-middle-class wife, however (whose bohemian childhood forms the basis of the novel, and film, Hideous Kinky) that he learnt about self-discipline. "Suddenly," he says, "I was with someone who imposed a work structure upon themselves. There we were, we'd just met and fallen in love and suddenly, even in my own flat, I was outside my bedroom waiting for two o'clock so I could go in and kiss her."

He is, he says, "crazily admiring" of novelists and painters and musicians, but faced with that kind of solitude finds himself "getting twitchy". He has done some directing (most recently Don't Worry About Me, a love story set in Liverpool) and has his own production company, Tubedale Films, but it's pretty clear that acting is and will remain his main career. Which is not to say that "looking back over the years" at his acting career he can't see any mistakes at all. The biggest one, and perhaps the most mortifying, was Basic Instinct 2. The whole process was so dismal that Morrissey seriously thought about giving it all up. "I felt bored by it, which is a terrible thing. And then I got depressed. It was my responsibility to kick arse and make it different and I didn't do that. It knocked me down."

As always, he picked himself up. Since then, he has done two more Hollywood films, The Reaping (with Hilary Swank) and The Other Boleyn Girl (with Natalie Portman) and is currently filming Centurion, a Roman fantasy adventure with darling-of-The-Wire-watching-media Dominic West. Also, of course, the Christmas Doctor Who, which gave him his first taste of the kind of fame that has people stopping you in the street. Would he like more of this?

Morrissey smiles, and I realise that I've hardly ever seen him smile. "I'm very happy," he says, "with the range of roles I get. I think you can get greedy as an actor. You miss what's happening right here, right now. We can sometimes get a little bit depressed about the stuff we're not doing." I'll take that, I think, as a "yes".

'Is Anybody There' opens on 1 May