When a nervous Michael Attenborough took artistic control of the Almeida from Ian McDiarmid and Jonathan Kent in 2002, he asked them if there was anything that they felt they had got wrong. Considering that they had put a small Islington theatre on the international map, starting with Diana Rigg's brilliant performance as Cleopatra in Dryden's All For Love, the answer was surprising. “Too many stars,” they chorused.

Well, there have been fewer stars on show during Attenborough's reign and those with star quality also have deep theatre experience. Think of Eileen Atkins, or Simon Russell Beale, or Jonathan Pryce making love to an animal in Albee's Goat. “Ian and Jonathan were very clever in their casting and weren't denigrating their actors,” Attenborough says when we meet in the Almeida's grotty old offices. “But they knew that stars unbalance expectations. If one show has a star and the next doesn't, there's a danger of people bypassing it.”

Attenborough has just announced more than a year's programming, and the one obvious star he's cast so far is Juliet Stevenson, who plays a musician somewhat like Jacqueline du Pré in a revival of Tom Kempinski's Duet for One. Steven Mackintosh and David Morrissey, who appear as warring brothers in Neil LaBute's In a Dark Dark House next month, are fine actors but not household names. Whatever the cast of Jez Butterworth's new Parlour Song (“a very funny play about the sexual frustrations of lower-middle-class life”) and Shakespeare's Measure for Measure, the priority will be the show, not any show-off.

With a programme that includes five world or European premieres, Attenborough can't be accused of caution either. And since the Almeida has gone from deficit into surplus during his six years, averaging audiences of 85 per cent, his policy seems to work. He's an enthusiast: with words such as “thrilling”, “wonderful” and “fantastic” pouring out, he reminds you of his father, Richard. His life hasn't been without grief, for he lost his sister and niece in the 2004 tsunami, a tragedy that undermined the Attenborough family's sense of being blessed: “It's the worst nightmare, to bury your children,” he says. “You don't get over that. You can't.”

But his own children may have theatrical careers, with his elder son a Cambridge undergraduate who has just toured America in Henry V and his younger about to play Hamlet at school. And the Almeida is, he says, a huge relief after 12 years with the RSC that ended in 2002.

As a senior figure there, he became so fed up with internal politicking that he gave up his management duties but went on staging plays until just before Adrian Noble resigned as the RSC's supremo. He was asked to put himself forward as a replacement, but refused, largely because the board thought that a troubled company needed a money man as chief executive: “I totally disapprove of the idea of an artistic director submitting his ideas to an administrator. Any theatre needs a vision and that can only be supplied by a practitioner.”

Indeed, “scrabbling around for safety”, which is what the RSC appeared to want, strikes Attenborough as a recipe for disaster. That applies to the Almeida, too. In 2006 he revived Michael Hastings's T.S. Eliot play Tom and Viv, sure it would appeal to Islingston sophisticates. It flopped. Often, surprise has brought success, such as with Big White Fog, Theodore Ward's long-forgotten play about American blacks in the 1930s, or Stephen Adly Guirgis's Last Days of Judas Iscariot.

There have been failures and there are new worries, for the theatre relies on the Lehman charitable trust for the work with local secondary schools that Attenborough has instituted. Yet he still seems entranced with the Almeida. He can personally greet the 29 people the theatre employs instead of finding himself lost for the names of the 700 who worked for the RSC. He can produce what he wants on a stage that's wider than many West End theatres and in an auditorium where nobody is more than a few yards away.

And early this year he received a compliment that he values more than any other. It came from his hero, Harold Pinter, after the Almeida's revival of The Homecoming. “I was,” the Nobel laureate said, “chuffed to my bollocks.”

Booking for the new season opens tomorrow for Almeida supporters; public booking on Nov 5. (020-7359 4404; www.almeida.co.uk)

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