Mark Rylance arranges to meet me in the bar at Rada in London, apparently for logistical reasons: later this morning, this is where he will be holding auditions for his new production of Much Ado About Nothing. But from my point of view, it's an almost perfect venue. Where better to talk to the greatest actor of his generation than the place where he trained? On the way there, I picture crowds of beautiful, hollow-eyed students tumbling out of cavernous rehearsal rooms into gloomy corridors that smell vaguely of greasepaint – a childish fantasy that is nine parts Noel Streatfeild to one part Fame – and feel suddenly excited at the prospect of what a good dose of nostalgia might lead the lovable but sometimes rather eccentric Rylance to say.
But, of course, I have it all wrong. The atmosphere in the foyer bar is sleek and professional, all cappuccinos and chrome, and when I ask him what Rada was like in his day – among his contemporaries were Timothy Spall, Kenneth Branagh and Fiona Shaw – he is anxious rather than indiscreet. "I did love being a student," he says, looking round the room bemusedly. "But I was very lonely and intense. I'd read too many of the letters of Van Gogh, and too many of the poems of Rilke, and there was all this ridiculous stuff in my head. I had this idea: no pain, no gain.
"I hadn't been raised in the pub culture. I'd grown up in America [his English parents, both teachers, were working in Wisconsin] and pubs weren't places you went to. So the whole culture of how students met one another … I didn't know what that was about at all.
"The newspapers in Milwaukee were good when it came to local fires and the occasional murder, but there was absolutely no world news in them. While I was here, Mrs Thatcher came in, and then there was the miners' strike. There were lots of fantastic working-class, activist actors around me, and I was constantly embarrassed because I didn't know anything. I'd come from the midwest! It was exciting. But it was terrifying, too." He widens his eyes – so dark and shiny, they could be two chocolate Minstrels – the better that I will believe him.
Rylance's production of Much Ado About Nothing, to be staged at the Old Vic in September, will star Vanessa Redgrave as Beatrice and James Earl Jones as Benedick (Redgrave and Jones, neither of whom have played these roles before, were last on stage together on Broadway and in the West End in Driving Miss Daisy). Today, he will audition younger members of the cast. As depicted in the movies, auditions are shouty, humiliating exercises, usually of no more than two minutes duration. Rylance's, however, last up to 30 minutes each, and are designed to be encouraging rather than demoralising.
"I try to move them one way or another depending on how much they're coming out to me, or into themselves," he says. "Often, their nerves and desire to get the job makes them overly expressive – not bad, but they express more than they need to – so I'll give them some kind of an obstacle to stop them being so sure-footed. Then I'll see how they take that note, and I'll listen to their voice, try to tell whether or not it's locked in a particular place, and I'll look at their movement.
"Thanks to my casting director, it's very rare that people come in and can't do it. Sometimes, people will have had bad training, and I'll think: I'm going to have to unravel a lot here. But most can do it, and so then it's rather like looking at football players. You have to build the team, the company. My job is to try and sit in the audience's seat. I've got to think what the audience is coming for, and what they will get."
Redgrave and Jones are, he says, like two fine, old whiskies. "You don't want to put water on them. You want to have them as they are. I want them to bring as much of themselves to the parts as possible." But to be the boss of Vanessa Redgrave! How nerve-racking. "Well, I do get a little bit nervous with directing. There are so many strategic decisions to be made. It's like being a military commander. But I know Vanessa very well – I invited her to the Globe [he was the theatre's artistic director] to be in The Tempest – and we're very close. I love her presence."
Rylance was with Redgrave in New York in the weeks after her daughter Natasha Richardson died in 2009 following a skiing accident. "People would come up to her to express their condolences, and it was quite extraordinary to see how present she was in that situation. Her imagination sees no obstacles; it was her who got this [production] off the ground. She just loves to work."
He shakes his head, and grips the edge of the table. He doesn't say so, but it seems to me that he and Redgrave have this quality – a dignified and rather old-fashioned kind of stoicism – in common. In 2012, the younger of Rylance's two beloved stepdaughters, Nataasha van Kampen, died at the age of just 28, having suffered a suspected brain haemorrhage. And while this terrible loss meant that Rylance decided to pull out of the Olympic opening ceremony (he was replaced by Kenneth Branagh), he, too, clearly found work to be some sort of a balm. Three weeks later, he was back on stage, giving one of the richest and most plangent performances of his life as the villain in the Globe's all-male adaptation of Richard III.
Like many actors, Rylance was pretty much the opposite of a show-off as a child. "When I got into Rada, my parents were incredibly surprised. I was intensely shy; I couldn't speak until I was six." Pretending to be other people was, he says, a relief, his best means of expression. Were his parents supportive of his chosen career? "The only time they weren't was when I was in my first musical. It would have been in about 1972, and I must have been 12. It was called The Me Nobody Knows, and it was one of those musicals that had been researched in the community; it was about some kids in the Bronx. It was beautiful.
"In the those days, we had a VW van. I remember it very well. We were driving home to the suburbs, and I was sitting in the back, listening to my parents talk about the show. 'Oh, he was good,' they would say. 'Oh yes, and he was very good, too.' I gradually realised that they had named every single actor apart from me, and I didn't know why. It was only many years later that my dad confessed that they hadn't known what to say, that they thought I was terrible."
His parents were, he says, vastly different from each other. "Eventually, they separated. I know there are fears for young people when their parents split up, but there are benefits, too, from the pillars not being too close together: a creative space." Certainly, something went right. His sister is Susannah Waters, the opera singer and novelist; his brother is Jonathan Waters, the sommelier at Chez Panisse, Alice Waters's (no relation) famous restaurant in Berkeley, California. "That's his craft. I went camping with him in Utah for a week recently. He made all the food, and it was impeccable." (Rylance changed his name from Waters because there was someone already registered with Equity with that name.)
He began his career at the Royal Shakespeare Company and for the next couple of decades seems rarely to have been out of work (he and his wife, the composer Claire van Kampen, also founded their own theatre company, Phoebus' Cart). He won an Olivier award for his performance as Benedick in Thelma Holt's 1993 production of Much Ado About Nothing, and in 1995, he became the Globe's first artistic director. But it was the 21st century before he became really well-known. In 2005, he won a Bafta for his performance as the weapons expert David Kelly in Peter Kosminsky's The Government Inspector. In 2007, he appeared in the West End in the French farce Boeing Boeing, and when the play transferred to Broadway, he won a Tony for his performance as Robert.
In 2009, he was cast as Johnny "Rooster" Byron, waster extraordinaire, in Jez Butterworth's play Jerusalem, a performance that most critics thought the most thrilling they had ever seen in the West End – and when the play transferred to Broadway, he won his second Tony award. I interviewed Rylance in his dressing room after Jerusalem had transferred from the publicly funded Royal Court to the West End, and it was almost as if he had become Johnny; I remember him as being huge, and yet he strikes me now as elfin and rather delicate. Will he ever be the Rooster again? "I hope so," he says, with a grin. "I hope I'll do it many times."
The successful export of Jerusalem, a play that few believed would translate, is yet another reminder of the destructive nature of the government's cuts to the arts budget – though as Rylance points out, you have only to walk up Shaftesbury Avenue to be convinced that theatre is our greatest export. As he rode on his bicycle to Rada this morning, he passed both the theatre where Lenny Henry is starring in August Wilson's Fences, and the new home of the National Theatre's adaptation of The Curious Incident of the Dog in the Night-Time (a novel he loves). "The richness of it all is incredible. The cuts are terrible, so short-sighted. Thanks to Shakespeare and imperialism, this language of ours is learned and admired around the world. If ever there was an industry that was indigenous to these cloudy islands, where you can't find a spot of sun for the life of you, then it's the theatre. The cuts are insane, and symptomatic of the ridiculous mindset that believes the creative arts are just an indulgence."
Rylance appeared in 420 performances of Jerusalem, and yet he never seemed to fade; every night there were fireworks, a feeling for the audience that, as he puts it, "something had happened". (I saw it relatively late on, and for the first time in my theatre-going career spontaneously rose to my feet as the curtain fell.) How did he do it? How did he keep it so fierce? "Some productions are made in such a way that actors are not allowed to change or move things. The director says: 'That's it, I want it like that every time.' In my experience, it's very, very hard to keep the life in those productions – pretty soon, you're thinking about other things while you're doing it – and I avoid those kinds of directors now. Other directors – Tim Carroll, Matthew Warchus, Ian Rickson – are interested in the life of each performance. They make their productions to last, and not so brittle that they'll break. They encourage actors to surprise each other, to keep it fresh, to bring the sense of discovery and fun from the rehearsal room into the performance. You have to move into chaos. For the audience to have a sense that something has happened, there needs to be a fleeting moment of confusion."
It's for this reason that he hasn't seen the film of the Globe's all-male production of Twelfth Night (along with Henry V and The Taming of the Shrew, it will soon be seen in cinemas nationwide). In October, Rylance and the rest of the original cast, including Stephen Fry as Malvolio, will take both it and Richard III to Broadway (Rylance is a mesmerising Olivia).
"I wouldn't ever watch it," he says. "I don't want an outside view. It makes you a bit self-conscious. You think: oh, do I do that? And: that's not what I imagine I look like. Some actors do watch themselves. Kristin Scott Thomas watches early rushes, and then adjusts her performance. But I tend not to want to. I want to play free of that concern. I don't want it to obscure my listening, and my energy. After all, it's only a record of one performance. I'm always trying to clear my memory of what happened the night before. You, the audience, don't want leftovers; you don't want what I served the night before. With Shakespeare, the audience has so many fears and anxieties, so many preconceptions; you have to draw them into the present, to give them an experience rather than a lecture. It should be like a great tennis match: who's going to win?"
Richard III and Twelfth Night will run until February ("unless it comes off after only a few days… it's a brutal place, Broadway"), and then he'll come home to play Thomas Cromwell in the BBC's adaptation of Hilary Mantel's Wolf Hall. This is a big job – expectations will be huge – and he knows it. He's nervous. "I've been so busy, I'm only 100 pages into the book," he says. "The fluidity of her story-telling is amazing, but …" He frowns, and grips the table again. "It's a curious part because so much of what makes Cromwell interesting is what he doesn't say, and doesn't do. On film, that's going to be an interesting task."
Thanks to Broadway, then, he won't be around for most of Much Ado's run. But his wife, its associate director, will fly back and forth, and generally keep an eye on the production for him. "Claire watches my back," he says. "We're very lucky. We work together, and it has made us closer. You learn a lot from collaboration with a person you love: how and when to say things, how to criticise."
Van Kampen was the co-director of his play Nice Fish, which was staged earlier this year at the Guthrie theatre in Minneapolis (Rylance co-wrote it with Louis Jenkins, a poet from Duluth whose works he has sometimes quoted at awards ceremonies, somewhat to the bemusement of his colleagues). "She saw everything. Bang, bang, bang: after the first preview, we were able to lose 20 minutes thanks to her.
"The works become like children." A sharp intake of breath. "They're not as precious as children, but they are born and you try to do all that you can to prepare them to go out into the world." Smiling broadly, he flings his arms around me. Then he gathers his papers – his lists of actors, his hand-drawn plans of the Old Vic stage – and gets up to go. The next round of nurturing had better begin sooner rather than later.