Roger Allam is one of those actors with the rare gift for making an audience purr with pleasure. You depend on him to stroll on at the National or the RSC - where he has spent most of his career - in a Chekhov or a Molière, a Shakespeare or a musical, and decorate his performance with laconically cocked eyebrows and droll asides. He is the master of insincerity, the purveyor of oil and ooze. One day he will be the definitive Tartuffe.

But if Allam is that easy to fit in a pigeonhole, how come he keeps getting asked to play German chancellors? Three years ago he gave us his Führer in Speer, David Edgar's play about Hitler's architect. And now there's Willy Brandt, whose brief but brilliant career as West German leader in the early 1970s is documented in Democracy, a new play from Michael Frayn at the National. "It's like playing kings of England in repertoire," he says. "Next up, 'Adenauer: the Musical'."

Both politicians were crowd-pleasers in their way, but not in the way Allam is: after 25 years on the boards, people are starting to realise how good he is. His reward for winning an Olivier for a screamingly camp performance in Privates on Parade last year was a West End lead opposite Gillian Anderson in the (it must be admitted) abysmally received What the Night is For. And all being well, he will take on the complete and utter dastard Count Fosco next year in Andrew Lloyd Webber's musical version of The Woman in White.

But first there's Herr Brandt. It's easier to see why Allam was summoned into the distinguished club of (mostly ennobled) actors who have donned the toothbrush moustache. He saw, it himself in the mirror. "Making myself up as Hitler, doing the hair and the 'tash, I discovered a thing about his eyebrows. I took out the top of my eyebrows and drew them in lower and that was rather scary. Especially if I half-closed my eyes, I really looked like Hitler."

Brandt is more of a stretch: "You latch on to anything. His haunted face. The sense of guilt in that generation of Germans and also a fury that they have to be guilty, and a resistance to it. There's a sense of guilt in him that he got away in 1933." The first leftwing chancellor of post-war West Germany, and the first politician to make real diplomatic overtures across the Iron Curtain, Brandt is much the most decent man Allam will have ever played.

Admittedly there's not been much competition. You can just as easily see him as the play's other main character, a man called Günter Guillaume who wormed his way into Brandt's inner circle and turned out to be in the employ of the Stasi.

After nuclear physics in Copenhagen, Frayn and his regular director Michael Blakemore have set themselves another difficuIt task of finding drama in the most unlikely corner - this time, a post-war Bonn run by men who tacitly understood that they had no business being charismatic. On the page it is a dense read, and Allam nearly turned it down. "I just couldn't follow it. I remember when I saw Copenhagen, you thought, 'Oh God, have I got a whole evening of this? Then you relax and get into it.'"

Allam is the type of character actor who has grown into his face. Though he became a father only three years ago, he is just old enough to remember "playing on bombsites in the East End in the '50s". His father was a vicar, and they moved all over London. Allam was sent to Christ's Hospital, the charity school in Sussex.

"I was very stupid at that school. I was flung into this incredibly hostile environment and was in all the bottom sets. I was called Zombie. You had to call boys a year or two older than you Sir, and if you didn't they could beat you about the face and neck. One adapts to these things, but discovering acting was quite a liberation when I was 16 or 17. My school certainly made me feel quite at home in the RSC."

A good enough singer to play Javert in the original Les Miserables, he initially flirted with the idea of becoming an opera singer, but plumped for Manchester University to read drama, a couple of years ahead of Ben Elton, Rik Mayall and Adrian Edmondson. You suspect he gets asked about these household names rather too often for his taste. "People like to check," he says with the lightest of wasp stings.

His first job in the 1970s was with a company called Monstrous Regiment. "They were a group of women who got pissed off with their roles in companies like Belt and Braces and 7.84. I think I got it because I could play various musical instruments - piano, keyboards, guitar, bit of banjo and mandolin. I used to want to be a folk singer. Most folk clubs around London you could get in for free if you played a couple of songs."

There is something about Allam that is just fitted for theatre, something oaksmoked and seasoned about the noise that comes out of his mouth, something large about his presence, which may explain why success has come late and also why, give or take the odd bent copper, he plays so few contemporary roles. He doesn't look quite right in a denim shirt, or with a slimming plate of salad in front of him, in a small room or on a small screen.

"When you get to film and television they never know quite where to place you. They think, 'Oh yeah, but you were a drag queen, weren't you?' Or, 'You were Hitler.' And you don't look like either of those things when you come in the room. In television you just get sent stuff and you're just A Dad. And if the script was particularly deep and insightful it would probably be great being somebody who's just A Dad, because there might be something there. But very often, without wishing to f--- up future employment, all I can say is, 'There isn't.'"