Just conceivably you saw a familiar-looking man walking through Oxford recently, muttering to himself in an American accent and, by his own admission, looking “absolutely mad”. Should you have dialled 999? No, because it was Kevin Spacey rehearsing his lines for his performance in David Mamet’s Speed-the-Plow, which is about to open at the theatre he runs, the Old Vic in London. The Oscar-winning star of American Beauty was in Oxford because he likes to hop in a car or on a train and explore what’s now his adoptive country. And he was babbling away earnestly because he just can’t get lines into his head if he’s sitting in his Waterloo flat.

“But if I go to a noisy train station or noisy cafe or noisy bar with my script it forces me to focus. Plates are falling, babies are crying, phones are ringing, people are ordering, and I can retain things that I can’t if it’s too quiet. I may look like a crazy bum, but I’m learning, learning, learning, then closing the script and mumbling away.”

Perhaps he was also looking frantic and driven in Oxford, for he’s playing an independent Hollywood producer horrified to discover that his sure-fire project may be scuppered by Jeff Goldblum, as the studio executive, who has fallen for an idealistic secretary. It’s the sort of darkly comic situation he has encountered in film and theatre. The play, says Spacey, shows the conflict of art and culture with commerce and money-making – and is much concerned with the terrors that he felt as a young, aspiring actor and has observed in others.

“I went through a period early on when I was afraid of not being good enough to play in the leagues that I wanted to play in. There was a period when I became arrogant and self-inflated in reaction to my fear. Yes, I can recognise the desperation of wanting to make a mark. And I certainly recognise that there are scars, there are compromises, there are things you have to give up as a result of that level of ambition: meaning you can f*** up friendships if you are as driven as that.”

It’s largely because he understands the frustration of would-be theatre people that much of his energy at the Vic has gone into its educational and outreach programmes, principally the New Voices Club. That’s a network of 3,000 young actors, writers and directors that creates an annual 50 productions, gives help to theatres up and down the country and last year made a contribution to 54 offerings at the Edinburgh Festival: “When they told me, I was stunned. I said you’re kidding, you mean five. But, no, 54 were born out of New Voices.” But it’s as the Vic’s artistic director that Spacey has attracted the publicity, the plaudits and the brickbats. Some suggested that he took the job because his film career was faltering, not knowing that the initial decision was made when American Beautywas having its London premiere in 1999.

Famously, he took a cab to the South Bank, walked along the Thames and ended outside the Vic, where his anglophile parents had taken him to see Laurence Olivier in the 1970s and he had enjoyed enormous success playing the lead in O’Neill’s The Iceman Cometh.

He knew the stately old place had struggled for years to find an identity. He had also been drama-mad virtually from the moment he emerged from the womb and had wanted to run a theatre since he was 13: “And I just didn’t want to spend another ten years being on film locations and living in hotel rooms. I wanted a company and consistency and something beyond my own career. After all, things couldn’t get better after American Beauty. I thought: what am I supposed to do, spend the next ten years trying to top myself?”

Spacey, who is now 48, still expects to spend ten years at the Vic; but there was a time when that seemed unlikely. His debut offering in 2004 was a Dutch play called Cloaca, which means “sewer” and was seen by some critics as just that, and, after Ian McKellen had frolicked through the role of Widow Twankey in a Christmas Aladdin, Spacey appeared in an American comedy called National Anthems, which suggested to me that he hadn’t yet got his finger on the British pulse. A year later he had a serious flop with Arthur Miller’s satiric Resurrection Blues – though here I remain convinced that a worthwhile play was ruined by Robert Altman’s inept staging.

But there have been successes: Trevor Nunn’s staging of Richard II, with Spacey winning awards as the King; a revival of Moon for the Misbegottenwhich reinforced his reputation as the O’Neill actor; The Entertainer,with Robert Lindsay as Osborne’s seedy comedian; Diana Rigg in a stage version of the film All About My Mother.

The future looks bright, too, with Peter Hall’s production of Pygmalion en route, a revival of Alan Ayckbourn’s three-play Norman Conquests promised, and the launch next year of the “Bridge Project”.

This will bring Simon Russell Beale to the Vic and to Brooklyn’s Academy of Music in Sam Mendes’s productions of The Winter’s Tale and The Cherry Orchard. And Spacey wants to tackle more O’Neill and some Shaw, Ibsen and Chekhov: “I feel ready to try the unexpected and challenge myself, even if I fall on my face.”

Sitting in his brown corduroy suit in the Vic’s bar, Spacey seems at ease. He fends off inquiries about his private life, saying only that it’s “very, very stable and quiet”, that he doesn’t frequent parties or film premieres, that he tries to carve out time when he can visit art galleries or the English countryside: “I know we live in a world where a person’s life is used for entertainment or gossip, and I suppose it’s understandable that people are curious about how you live. But I was brought up to believe that there’s a professional life and a personal life, and that’s why they’re called that. So they’ll remain that way.”

But when he turns to professional topics, you can hear the ringing articulacy he perhaps inherited from his Welsh forebears and see the American energy that prefers to look optimistically forward than ruefully back. Certainly, he’s unapologetic about the Vic’s offerings to date, admitting that Cloaca and Resurrection Blues didn’t fulfil his hopes but declaring that, if he’s to make the theatre a necessary destination again, he can’t stage only classics. He can’t try to please an elite that, he says, wouldn’t have been happy “unless I’d come riding down Waterloo Road on a white horse with Olivier standing on my shoulders”.

“I wouldn’t change anything we’ve done because we’ve done everything honestly,” he goes on. “Every decision we’ve made has been in the spirit of wanting to be entertaining and different from what some critics expect on the Old Vic stage.

“The ordinary punter doesn’t come here knowing this theatre’s great history, and we are not programming for anyone’s narrow vision. We’re programming for a 1,000-seat theatre and we’re trying to build a new, younger, more diverse, broader audience.

“People have written asking, how dare we do pantos? But that is going back to its traditions. It’s been a music hall and it did Aladdin in 1860. And at the final performance of Stephen Fry’s Cinderella the other night, the place was packed to the rafters.” And, yes, a policy that consists of attracting top talent to the very varied shows that Spacey finds interesting – he cites the National’s former supremo, Richard Eyre, who told him “I did the work I liked” – seems to be proving effective.

In Spacey’s two-and-a-half seasons as its director, the Vic has sold 950,000 seats and is keeping financially afloat, all without subsidy. Which isn’t to say Spacey is against subsidy for others. Quite the contrary. Anyone who doubts that he’s become a committed member of our theatre community should hear him on the Arts Council and its proposed cuts. He went to a recent meeting of objectors at the Young Vic and was left thinking the council’s behaviour “outrageous” and its arguments “evasive, stone-walling, incomplete and nonsensical”. In his view, the Government should intervene, ordering a national theatre review before bad decisions get finalised.

Not that he’s renounced America. He keeps an apartment in New York. He’s a friend of the Clintons and, though unwilling to endorse Hillary, is finding the race for the White House the most enthralling he can recall. He also brought Moon for the Misbegotten from the Vic to Broadway and has taken time out for the occasional film, recently 21, about how six university students stung Las Vegas for millions, and an HBO docudrama about the aftermath of George W. Bush’s victory over Al Gore. I got the feeling that one day he might run a New York playhouse – though he says that America’s powerful theatre unions would make any such endeavour a misery.

But meanwhile, he’s rehearsing Speed-the-Plow and finding that it’s largely about the language below language: “Masks, codes, shorthand, double meanings, triple meanings, what people are actually saying and not saying.” He’s also working hard to put and keep the Vic on the theatrical map, whether that means giving it a cultural identity or renewing its Victorian plumbing and leaky roof: “I want to build somewhere that will continue to produce for 50 years. I want to leave the next artistic director a war chest so he won’t have to go out fundraising. I want to ensure there’ll be an actor’s theatre here that will survive long after I’ve gone.” Well, maybe he’s the man to do it.

— Kevin Spacey presents the South Bank Show/The Times Breakthrough Award on ITV1 on Sunday at 10.40pm

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