A 21-year-old student actor sneaks into the Old Vic. He’s relatively new to the UK, having left his family in South Africa three years earlier. It’s 1971 and Laurence Olivier’s National Theatre Company is reviving Carl Zuckmayer’s 1931 satire The Captain of Kopenick. Paul Scofield, giving one of the performances of his life, is playing Wilhelm Voight, the convict shoemaker who, unable to carve out a life for himself, dons army clothing and takes charge of a group of soldiers and storms the town hall.

You get this nonsense about us being luvvies. It’s complete rubbish. They should learn a big Shakespeare part and stand in the wings. I’ll happily clean up whatever bodily fluids they leave behind

This month, that very student will slip into Voight’s fraudulent uniform for the same company. “It was one of the first plays I saw over here,” Antony Sher recalls, his fingers twiddling the stem of a post-rehearsal glass of white. “Scofield was astonishing in it. I was very lucky that I arrived in this country just in time to see a few of the all-time great actors onstage and, in a way, Scofield amazed me more than any of them.”

In the intervening years, Sher has unquestionably earned his place among those greats. Several of his Shakespearean leads – his guilt-wracked Macbeth; his muttering Shylock; that ‘bottled spider’ of a Richard III – have gained canonical status. Voight nestles snugly on a CV that includes Khlestakov in Gogol’s The Government Inspector and Dr Stockmann in An Enemy of the People. Like them, Voight has a subversive quality capable of wreaking havoc among local authorities.

However, Sher sees him in a wider context: “In this massively bureaucratic world, Voight is the man without papers, without identification. He’s totally lost, totally powerless until he gets that uniform on.

“He’s the outsider, which I’m very drawn to playing because, being gay, Jewish and a foreigner in this country, I’m an outsider myself.” It’s the prism through which he sees most characters – insider or outsider. To Sher, Shylock and Richard III, for example, are first and foremost “outsiders so damaged that they become dangerous… It’s just something I understand.”

“People say: ‘You’re working at the National Theatre. You’ve got a knighthood. How can you possibly be an outsider?’ I can only answer that, deep in me, I’ll always be an outsider because that’s how I grew up.”

Such, he says, is the actor’s lot. “We do a job that people don’t understand, so you get this nonsense about us being luvvies. It’s complete rubbish. They should learn a big Shakespeare part and stand in the wings. I’ll happily clean up whatever bodily fluids they leave behind.”

The idea of the stage as a place of trauma carries considerable weight with Sher, who mentions research that the actor preparing to go on has the same adrenaline-levels as a car crash victim. He has written eloquently about his own experiences of stage fright, which “can easily cripple you.” He tackled it with a demon-facing solo-show, the acclaimed Primo, also at the National.

Antony Sher as Richard III in 1984 at the Barbican. Photo: Reg Wilson

So, it is strange to hear him root the urge to act – his own and others’ – in shyness. “A lot of actors are introverts. It leads them to do this strange job, standing in front of people saying, ‘Look at me.’

“What drew me to acting in the first place was disguise. I was a weak kid, not good at what all the boys at school were good at and I found that by acting, by being other people, I could liberate myself from those inadequacies.”

Read his account of creating Richard III, entitled Year of the King, and you realise the painstaking diligence in the process of disguising himself. Sher recorded hours of nature documentaries in search of mannerism and ticks, sketched postures and deformities to piece the man together.

Over time, however, he’s moved towards acting as a form of self-expression alongside his writing and painting. “Perfect example,” he blurts suddenly, “Judi Dench. She seems to open her soul in every role she plays.”

Behind this is the need to keep growing as an actor. Sher cites Richard Burton as a warning – he’s reading the diaries at the moment. “He became one of the most boring actors imaginable, because he stopped being curious and started to play Richard Burton. He just became more and more bored by acting.”

There’s no chance of that with Sher. The creative process, ineffable and unpinnable as it is, evidently fascinates him enormously. “Every play I do, every book I write, every painting I paint, I will struggle with. I don’t know what it’s like for a project to come easy.”

There is, of course, one tiny hurdle left to secure a position in the pantheon – Mount Lear. Scofield topped it, of course, and so too have Sher’s old rep colleagues, Jonathan Pryce and the late Pete Postlethwaite. “There isn’t another one left, really,” he says, with a note of sadness. “I’m sure I’ll be back at the RSC, since my partner [Gregory Doran] now runs it. At least, I hope he’ll give me a chance.”

The Captain of Kopenick runs at the Olivier, National Theatre, London until April 4