It is an actor's job to be other people, but usually they are characters of his and the playwright's imaginations. Having to take into account the facts of a well-known figure's life calls for a different way of building a role, as Roger Allam is finding in his preparation for the lead in Michael Frayn's Democracy, which opens at the National Theatre's Cottesloe next week. He will play Willy Brandt, the mayor of West Berlin and Chancellor of West Germany and the winner of the 1971 Nobel peace prize for his Ostpolitik, the policy for healing the breach between East and West.

Allam will have to compete with older theatregoers' memories of the immensely popular Brandt, who had the actor's gift of controlling a crowd, even without using words. His kneeling at a memorial to the Jews of the Warsaw ghetto made a huge impression around the world. And all who pass "a great big poster with Willy Brandt's face on it on their way into the theatre," Allam says when we meet during rehearsals, "will notice that I don't look much like him." But he doesn't feel it necessary to make his features look more angular or to recreate Brandt's double troughs of balding skull. "The jury's still out", he says, "on the make-up and hair."

Nor will he be trying to sound the way Brandt did when he spoke English. An accent, he thinks, "is a useful thing sometimes, and sometimes it isn't. You want it to assist the performance, not take it over." When he played Kierkegaard recently, in a radio drama, he made no attempt to sound Danish - Meryl Streep, one imagines, would have been horrified. More important, he says, is the character expressed in the voice, even when the voice of the original isn't known. When Allam played Cromwell on television, he constructed a voice based on the rhythms Cromwell used in his writing.

Along with listening to tapes and watching film of Brandt, Allam has been reading his memoirs and other books about the period that shaped him. "I've had enough time to read around the character. One book I've found useful is Sebastian Haffner's Defying Hitler, a quite ordinary man's account of the years between the wars.

"As so many people seem to have done," Allam continues, "I kind of fell in love with Willy Brandt. He was a genuinely good man. But there was an awful sense of melancholy about him. I think what comes over in the play is a sense of loss, his father never having been a presence in his life and his mother not much of one."

Brandt, who did not know his father's name until, in his thirties, he asked his mother, was brought up by his grandparents. He was also affected by his exile from Germany during the Nazis' rise to power, and by the war, when he worked abroad for the resistance. "I feel there was a strong sense of guilt that he wasn't around during those years," Allam says. "He absorbed conflict within himself in a passive-resistant kind of way."

The guilt of the survivor, Allam agrees, may have influenced Brandt's decision to resign when it was revealed that his assistant, Günter Guillaume (played by Conleth Hill, of Stones in His Pockets), was an East German spy who had evidence of Brandt's infidelities with a great many women. The security breach was not his fault, and he was probably popular enough to have faced down the sex scandal, but it was characteristic of Brandt to feel that he had to fall on his sword, though mass murderers among his countrymen escaped justice and prospered.

That is one of the many ironies of Frayn's complex play about a nation trying to renew itself after losing a war and being split by the Soviet occupation of the German Democratic Republic - its name, of course, another irony. "The play is saying that democracy, though it's bitchy, messy, and not a very efficient way of going about things, is in the end the best we've got. The play sort of celebrates that mess."

Allam's only previous stage portrayal of a historic figure, three years ago, was a real jump into the deep end. "I originally turned down Hitler [in David Edgar's Albert Speer] because I needed some time off, but a few months later Trevor Nunn called up and pleaded with me, saying, 'He's only in half the play.'" Ironically, the situation put Allam in a position of power that helped him in playing the role of the dictator. "Because of the lack of time I was able to..." (he raises a hand behind his head and, with a look of supreme indifference, snaps his fingers) "... I could say, 'Get me this, get me that, get me the home movies Eva Braun made of Hitler at Berchtesgaden.'"

Did he have no qualms about playing a universally known figure, whom he resembled even less than he does Willy Brandt? "Well, in that case his appearance worked in my favour. His is such a famous mask that, when you do the hair and the moustache, you're there. Everybody understands that the forelock and the little moustache mean Hitler, and then you can do what you like. I didn't even put on a German accent. I just made my voice slightly guttural and faintly northern.

"Also, the play being done in the Lyttelton meant that I could get away with effects I wouldn't attempt in the [much smaller] Cottesloe. I covered the top half of my eyebrows and drew them thicker underneath so they were very close to my eyes. That made enough of a difference for me to scare myself when I saw my reflection." Allam thought the effect too good to keep to himself. "I would wander around backstage, freaking people out." During a performance of one of the other plays then on at the National, an actor might glance into the wings and meet the stern gaze of the Führer.

This deadpan confession of mischief is no surprise to anyone familiar with Allam's stage presence: he's the best Mr Darcy we've never had. A mainstay of the RSC and later the National, he has been known for the sort of role for which he won the Olivier award for best supporting actor in 2000: the repressed Victorian in Money, who doesn't so much fall in love as slide into it by imperceptible degrees. In Troilus and Cressida he was the sardonic observer Ulysses, and in The Importance of Being Earnest he played the straight arrow Jack Worthing. However, his quintessential part was probably Benedick in Much Ado About Nothing, whose capitulation to romance was preceded by lots of offensive-defensive manoeuvres. Allam finally won the best actor award last year for playing the divinely camp female impersonator in Privates on Parade.

Was it partly in recognition, does he think, of his taking on a role so wildly against type? "Not exactly," he says, "but that was a very busy part - there was a lot to do, a lot on display, such as wearing a dress, and audiences and critics notice that." There is a slight pause before the word "critics", into which, one feels, one is meant to insert "even". But it's understandable that Allam sometimes despairs of his reviewers appreciating what he does. Half of his notices for Benedick, for example, characterised his performance by describing an effect - puffs of cigar smoke emerging from the hollow tree where he was hiding - that was created by the prop department. "With Brandt, on the other hand," he says, "his refusal to engage in argument is sometimes the most telling thing about him."

Since his appearance in the West End opposite Gillian Anderson last year in What the Night Is For, Allam's recognition has increased, but perhaps not with the most discriminating sector of the theatre audience. A pay-to-view celebrity-scandal website now offers what is apparently an unauthorised photo from that play, with the come-on: "Roger Allam NAKED!" Allam, who hadn't heard about it, is shocked, disgusted and horrified, and just wants to know one thing: "Where are my royalties?"