Trevor Nunn: Hey! Who are you calling a great director of musicals?

He did 'Cats' and 'Les Mis'. Then he ran the National Theatre. What's next for Trevor Nunn, asks Veronica Lee

It's strange how some major theatrical events come about. Take Trevor Nunn's latest project, Ibsen's rarely performed The Lady from the Sea, starring Natasha Richardson, the opening production of the newly refurbished Almeida Theatre in north London. It was conceived in a supermarket aisle. "I wanted to do it two years ago on the South Bank and for all sorts of reasons it didn't happen," says Nunn, who has just completed a six-year stint as the National Theatre's artistic director. "I know Michael Attenborough [the new director of the Almeida] well – we tend to meet on a Saturday morning at Marks and Spencer's in Chiswick when we are both doing the weekly shop, which is a strange place to discuss theatre, but there it is. When Michael took over at the Almeida he asked me to do the opening production and I said the ideal work was this."

But before that momentous evening, Nunn will be involved in another, being the inspiration of and honoured guest at The Night of 1,000 Voices at the Royal Albert Hall, a charity gala of songs from his musicals career, which includes the long-running Les Miserables, Cats and Starlight Express, plus Chess, Nicholas Nickleby and Sunset Boulevard, as well as more recent productions such as South Pacific, My Fair Lady and Oklahoma!.

Any attempt to pigeonhole Nunn as one the 20th century's great directors of musicals, however, meets with polite disagreement. Rather, Nunn is at pains to point to the diversity of a career that has covered Shakespeare, the classics and new writing as well as musicals. "I've done about a hundred productions and by far the minority are musicals That said, the contradiction between legitimate drama and musical theatre goes all the way back to my childhood.

"I came from a working-class background and my first encounter with theatre was variety on radio and vaudeville theatre, and the first show I directed [in the sixth form at grammar school] was a revue." But he clearly admires those musical-theatre performers able to cope with the extra technical demands that the genre place on them. "I think the levels of skills and insight required are as fine as anything that we associate with performances of a major classical work." Like it or not, though, Nunn's name will be forever linked to the rebirth of musical theatre, as well as a coals-to-Newcastle period when the British appeared to be teaching Broadway a thing or two about the form. Not for the first time in our interview, Nunn bats off the praise. "Cats going to Broadway coincided with a consensus view that American musical theatre had stagnated. Some people said to me, 'How dare you,' because it was quite revolutionary in its format and it was resisted in some quarters. But it explored the breaking of the barriers between the stage and the audience and it was a very thrilling experience that communicated differently with them." Nunn's association with musical theatre has a less esteemed side, though: the money he made when hugely successful shows transferred from the subsidised Royal Shakespeare Company and the National Theatre to highly lucrative commercial West End and Broadway runs. It's something that rankles among many who work for pitiful salaries in the theatre and Nunn was recently taken to task by Sue Lawley on Radio 4's Desert Island Discs. When pushed to explain himself, he made the extraordinary announcement that he was making a donation of his earnings – £2.5 million over three years – from said transfers to the National Theatre.

So did he exonerate himself? Not quite. It's rumoured that nobody at the National knew of the announcement beforehand and why talk about an act of private charity on national radio? Nunn himself refuses to be drawn on the subject, batting off questions with a polite but dismissive: "It's not anything I'm interested in highlighting." He continues: "I really don't want it to be made a fuss of. There's been a perfectly straightforward and entirely accepted practice about work transferring to the commercial sector ever since Arts Council subsidies began. What I feel is important is that it shouldn't be made a requirement of directors that it should be what they do, too." Indeed, not: Nunn's successor at the National, Nicholas Hytner, has stated that he will not personally benefit from commercial transfers.

I ask Nunn if he has popped over to see his ex-colleagues at the National (rehearsals for The Lady from the Sea have been taking place at the Old Vic, just a short walk from his old stamping ground). "You all say goodbye with a stiff upper lip," he replies. "It's a great irony that they are only 300 yards away and of course I should pop in and have a cup of tea with them. But you know that would be a terrible thing because you would be somehow an eminence shadowing somebody else's regime." The money debate is a sad full point to a successful period at the National (which he left in the black), but a mere blip in a long and distinguished career of a man who shows no signs of heading for retirement. Nunn, 63, outlines his diary for the next two years. "I shall do a new musical work, and then a play for children, then a Shakespeare, then a television production of a great modern classic, then a musical work on Broadway." But for today, at least, he can sit back and enjoy being in the audience for once as he is feted by an industry grateful for his huge contribution to British musical theatre.

'Night of 1,000 Voices': Royal Albert Hall, London SW7 (020 7589 8212), today. 'The Lady from the Sea': Almeida, London N1 (020 7359 4404), Thursday to 28 June