Trevor Nunn

Trevor Nunn: an eventful career. Photograph: Eamonn McCabe for the Guardian

When Trevor Nunn was about to take over at the National Theatre, his predecessor Richard Eyre records in his diary that Nunn gave a brief rallying speech to the troops. It was a taxi-driver story. "'You're that Trevor Nunn, aren't you?' the driver asks. "You directed Sunset Strip. And all that Lloyd Webber stuff. Now you're going to the National Theatre. Tell me, Trevor, what went wrong?'"

It's a witty story, deftly self-aware. The question has, at various times and in various forms, frequently been asked of Nunn, who is one of the most respected yet divisive figures in British drama. He may have been the boss of the Royal Shakespeare Company for a record-breaking 18 years (1968–86), then the head of the National for another six (1997–2003); but there are some who lament that he long ago sold out to commercial theatre. At one stage, the three longest-running shows of all time – Cats,Starlight Express, Les Misérables – were all his, and his critics allege that he has never been the same director since. On the other hand, there is no doubt a hard core of fans who wish he wouldn't waste all that time with Shakespeare and Chekhov, and devote himself full-time to musicals.

Nunn has been in residence at the Theatre Royal, Haymarket, for the past year or so, a strictly fly-by-night arrangement that has involved him directing four plays: a revival of Terence Rattigan's rarely seen wartime drama Flare Path, a transfer from the Chichester festival of Tom Stoppard's Rosencrantz and Guildenstern Are Dead, a new version ofThe Tempest, and now The Lion in Winter – a creaky historical drama about Richard I and Eleanor of Aquitaine, chiefly known via the 1968 film adaptation, which is to be the theatre's festive show (stagehands are busy heaving a Christmas tree into place when I arrive).

Again, no one seems able to make up their minds about whether this – Nunn's first artistic directorship since leaving the National – has actually been a success. He was effusively praised for bringing Flare Path out of mothballs (more than one critic admitted it left them in tears), and the response to Rosencrantz and Guildenstern was by no means wholly negative, but the reviewers seemed baffled by his sweet-toothed take onThe Tempest, which featured the cast prancing around in body stockings, as well as a synthesised musical score. "As kitsch as anything I have encountered in Holiday on Ice," harrumphed the Daily Telegraph's critic; "soft-focus, sugar-coated and gooey-centred," wrote the Observer's (not that this stopped the show, which starred Ralph Fiennes, being the hottest ticket in town).

It is hard to judge, then, as he and I settle down in a small office inside the theatre, whether Nunn – charming but faintly distant in person – is a director at the height of his powers, or a man running on fumes. He somehow seems capable of being both at once.

There is little in his background to hint at the career that would follow. Born in the bleak winter of January 1940 to a father, Robert, who was a cabinet-maker and a mother, Dorothy, who trained as a seamstress, Nunn grew up in a working-class household in Ipswich. Among his earliest memories is the Anderson shelter dug in the back garden. When his father suddenly appeared on the doorstep during the war, Trevor and his older sister Stella were petrified, Nunn recollects: "I have very distinct memories of him coming back after two years in uniform and not knowing who he was."

Although he is effusive on the subject of his family, it was not a comfortable upbringing: money was short and Nunn's father was sometimes out of work. "I was very aware that we had to be frugal," he says. "My mother made us clothes, my father did an enormous amount of work in the little house we had. Those things could not have been done were it not for him saying that he'd do it himself."

Were they worried about him going into that notoriously unstable profession, the theatre? "Actually it's the opposite of the usual story. When you don't have anything, and you say to your parents that you want to go on stage, they say: 'Great!' Because there's that possibility of escape, isn't there – the possibility that something can happen."

He made his theatrical debut at the age of five, in a nativity play ("the teacher said to me, you're a real actor … it became a family joke"), and when he arrived at Ipswich's Northgate grammar school, he threw himself into drama. One teacher in particular was an inspiration, Nunn recalls. "He just had this incredible ability to unlock the texts. Every year he directed the school play. Wanting to impress him, and wanting to emulate him, was very much part of growing up. In the sixth form he would do Friday night extra Shakespeare sessions. We would all bicycle out to his windmill."

By then Nunn had also ventured into professional drama, getting work with the local rep company at the age of 13. It was a life-changing experience, not least because one of his co-actors ended up being cast in the now-famous 1957 production of The Tempest directed by the youthful tyro Peter Brook and starring John Gielgud. Nunn travelled to the West End to see it, and even managed to sneak backstage.

In 1959, he won a scholarship to Downing College, Cambridge – not far from Ipswich geographically, but an entirely different world. FR Leavis was then in residence at the college, and Nunn promptly fell under his spell. "There were 12 of us," he recalls. "We were generally referred to as the disciples." Was Leavis as theatrical as his reputation? "Oh yes, irascible and eccentric and funny as well, very caustic. The hush and excitement, being in the presence of that mind, was extraordinary."

It appears to have been a time for reinvention: the Ipswich accent went (though only because it didn't play well with female students, Nunn insists), and he threw himself into the Cambridge theatre scene, part of a remarkable generation that included Derek Jacobi, Ian McKellen, Corin Redgrave, Peter Cook, David Frost and John Cleese. "During my finals term I directed both the Marlowe Shakespeare and the Footlights revue, so you can tell where my concentration went." He graduated with a 2:2; a happy trade-off, he says, for 34 productions – acting, directing, writing.

There was little doubt that he would end up in the theatre. Soon after leaving in 1962, he was taken on at Coventry's newly established Belgrade theatre as an assistant, filling in as an actor ("I wasn't bad") as well as directing his own professional shows. Quite a remarkable ascent, I say. "The first really big production I did, Brecht's The Caucasian Chalk Circle, was a show that London reviewers came and talked terribly enthusiastically about, but at the first-night party there was one middle-aged actor who lifted his glass and said: 'Here's my pledge, never to work with university directors again.' There was a ghastly silence."

Even more rapid promotion was to come. Nunn had frequently hitchhiked the 20 miles from Coventry to Stratford-upon-Avon to catch the productions of the nascent RSC, founded the year before by Peter Hall; little did he imagine that Hall, 10 years older, would pay a return visit and ask him to jump ship. Nunn laughs. "I had the lunatic nerve to say I'd rather not at this juncture, because I'm doing my own shows at Coventry. Eight months later I got a message from him saying he wanted to see me in Stratford. He said: 'I'm going to take you on as a director.'"

The RSC remains an integral part of Nunn's DNA; indeed, he's sufficiently wary of creating a fuss in Stratford that he refuses to tell me who he'd like to take over when Michael Boyd leaves next year. As well as forming the central phase of Nunn's career, the company cemented some of the most important relationships of his life – obviously with his mentor Hall, but also his first wife, Janet Suzman, whom he cast in The Taming of the Shrew in 1967 and married two years later. He remembers proudly the collegiate atmosphere. "We associate directors would take it in turns to discuss and notate. David Jones and I got on fantastically well. Also John Barton, my friend Terry Hands."

When Nunn arrived in 1965, he had little inkling that Hall, exhausted by getting the company through its first years, was nearing the end of his tether; two years later, when Nunn was just 27, Hall asked if the younger man wanted to take over. Nunn claims to have been flabbergasted, and refused three times. He comes across in Hall's diaries as a bit of a worrier, I say. He seems speechless. "I do? Well, I was very young, and when someone comes to you and says it'd be good if you took over the biggest theatre company in the world, it sure gives you pause." Was he genuinely that unambitious? "Never crossed my mind," he insists. "It wasn't panic. I thought I was being sensible. Peter agreed he'd come back after a bit." He laughs ruefully. "And then of course completely disappeared."

Perhaps it was just as well he did; while a rejuvenated Hall threw his formidable energies into moving the National from the Old Vic to the South Bank, Nunn got on with remoulding the RSC. It wasn't a period without its challenges – in 1973 he had to leave the company briefly because of suffering from what was called "nervous exhaustion" (he had, he says, taken to sleeping in his office) – but one of his most significant legacies was diversifying the spaces in which the company performed.

The company's stint at the Barbican (1982–2001) never seemed fully happy, yet the creation of Stratford's mid-scale Swan theatre in 1986 was a triumph: a demonstration that the RSC could do intimate as well as epic. Twelve years before, in 1974, Nunn had opened the Other Place, a tiny former storeroom in Stratford where young directors could emulate the experiments then being conducted on the London fringe; then, in 1977, he pulled a similar trick at the Donmar Warehouse in Covent Garden, which had been used to store fruit until Nunn and his team spotted its potential.

It was in these petite paired spaces that Nunn scored one of his career highlights – a famous version of Macbeth with Judi Dench and Ian McKellen, created on a design budget of £250, which enclosed the action in a tiny chalk circle, bringing out the play's claustrophobic, unearthly danger (some of which is captured by a 1978 TV adaptation). "Doing it to 200 people," he reflects, "we felt that something revolutionary was going on. There was no interval, and so in effect the audience were locked up with two people contemplating murder. The tension became extreme."

Although Macbeth showed that Nunn was capable of creating up-close psychological intensity – something also demonstrated by his 1987 version of Othello, with McKellen opposite Willard White – it was at the RSC that he began to search for broader canvases. In 1980 he brought to the stage a gargantuan, garlanded nine-hour version of Dickens'sNicholas Nickleby; a year later, in the West End, came Cats – an immersive musical spectacular where the audience sat inside the rubbish tip inhabited by TS Eliot's felines (albeit as tunefully re-imagined by Andrew Lloyd Webber).

Why did a director who could achieve so much with so little want to expand into musicals? "The first proper theatre I saw was pantomime. My theatregoing was always a mixture, going to see classical plays and seeing shows in town. I've never seen any dividing line, and I don't think Shakespeare saw one."

Certainly, through the 80s, the musicals kept on coming: Starlight Express (1984), Les Mis (1985), Chess (1986), Aspects of Love (1989). Some would doubt that they rank alongside the great plays he's directed. He begs to differ. "The skills involved in working with a musical score and lyrics, people who act, sing and dance, are every bit as particular as the skills required in putting on a Shakespeare play."

Fair enough, but that's not quite the point. Nunn has long been dogged by the criticism that his directorial talents (undoubted) have been at war with his taste (questionable). This returned with a vengeance when he ran the National, a job that Nunn once compared to "juggling plates, while riding a unicycle, on a tightrope, over Niagara Falls". According to the press, it seemed as if he couldn't do anything right: the perception lingered that his programming was too ratings-chasing; in 1999 there was even a squall about actors using hidden radio microphones to deal with the acoustics of the Olivier (this no longer happens). After two new plays were dropped and an adaptation of The Beggar's Opera failed,newspapers – including this one – called for his head.

When I ask about this, there's an agonising pause. "Something seemed to me to have been decided by various elements of the press right from the outset. But I didn't even apply for the job." How so? "I was begged to do it. I was absolutely clear that it was a holding operation. My task was to try to get it on to a financial even keel and to keep all the auditoriums flourishing." He adds defensively: "We won more theatre awards than the NT had ever won before, or has done since."

What about the accusation that his failing was to mistake populist for popular, filling the place with musicals such as Oklahoma! and South Pacific rather than more challenging work? He looks peeved. "I'd planned for three extraordinary new plays by Tom Stoppard called The Coast of Utopia, then South Pacific, but Tom then said the plays weren't ready, so I had time that had to be filled." It was all just a scheduling issue? "It was a lively period of time."

Almost as lively, recently, has been Nunn's personal life, which has taken some intriguing turns. After divorcing Suzman in 1986, Nunn married the actor Sharon Lee-Hill (the marriage lasted until 1991), then, in 1994, Imogen Stubbs. In April 2011, Stubbs announced that they were to separate; more surprising, she declared that she had been in another relationship "for a while". Then Nunn was pictured enjoying a holiday with the former partner of Sven-Göran Eriksson (and latterly Strictly Come Dancing contestant) Nancy Dell'Olio. A feeding frenzy gleefully ensued, perhaps fuelled by the assumption that it was somehow undignified for a man in his 70s to have a love life.

It sounds complicated, I hazard. He crosses his arms defensively. "My marriage effectively ended two years ago. That's all you're going to get me to say on that." And Nancy? "My involvements have been many and various over the last two years. Private is private."

OK, another cheeky question. He's made a lot of money from theatre over the years. How much? "Well, the first piece of commercial theatre I did was Cats. So of course that produced" – he chooses the word delicately – "revenue." Is he a millionaire? "It's been alleged." Still a Labour donor? He looks slightly furtive. "I was a major donor for a particular period of time." (This was during the early Blair years.) "My vote has never changed and can probably never be changed, because of the influence of my father."

So, a dyed-in-the wool, Labour-voting millionaire – and, since 2002, a knight. One of the best living directors; also, sometimes, one of the worst; a reluctant impresario, but a fierce defender of his record; a lover of the toughest classic drama, and also of shameless sentiment. As a life in theatre goes, it is certainly eventful. Where did it all go wrong – or right?