If Branagh seemed to make the succession look ripe for the taking, this was because he had just triumphed in the field of Shakespeare as Henry V, one of the young Olivier's signature roles. Also, like the indefatigable Larry, he was into everything: acting, directing, adapting, forming companies. Here he is now, two years off 50, preparing to be one of Chekhov's most garrulous idlers, Ivanov. Surely he can't have morphed from Prince Hal to Falstaff in this middle section of his dramatic life.

Looking back to that time of sudden prominence, he says that things moved so fast that he was approaching it all day by day, relying on instinct. "Because of the relative impact of what I was doing, because of that ubiquity, I suppose people thought there must be some sort of plan. What there was was an extraordinary amount of energy.

"Without that energy," he goes on, "one might have done things differently. Of course, one didn't just walk into things that were in front of one. What might be consistent between then and now is being passionate and energised about the things one loves."

These things, he insists, include live theatre as much as ever, and on the evidence of his present activity there is no reason to doubt him. He is now embedded with the director Michael Grandage's Donmar Warehouse, and Ivanov is the launch production of that theatre's year-long residence at the much larger Wyndham's. After a Twelfth Night with Derek Jacobi as Malvolio and a Madame de Sade starring Judi Dench, this residence culminates in Branagh turning director once more for a Jude Law Hamlet. He has already been working on this for the past year, meeting Law regularly to discuss the play, and when it is out of the way, he says, he has no idea what he will do next. He never did. When he says: "What else emerges will become clear," it sounds more plain than cryptic.

With such front-loaded careers there is always the temptation to diagnose some strain of burn-out or a slow slippage into Chekhovian disaffection. There are no such symptoms in Branagh, who is both chirpy and dogged. Instead he appears relieved that he is not as extravagantly famous as he once was. After his Henry V, for which he was showered with awards, he and his actress wife Emma Thompson occupied a place in the public gaze somewhere between Burton/Taylor and Becks/Posh. When they divorced in 1994 and he took up with Helena Bonham Carter, the interest remained intense. And when that was replaced by a relationship with her friend Lindsay Brunnock, to whom he is now married, his life turned to soap, and the tabloids lathered themselves in it.

"That's just the way it is," he says. "On the whole though, living in the real world, I am happier talking mostly about what I do rather than who I am. The prestige of celebrity for its own sake is not something that interests me. Although one can't be wallflowerish about it. One does work that one wants people to see. It is only complete when there is an audience. That's the event, whereas celebrity these days is inevitably the cost of the instantaneous and brief nature of most of the ways in which information is disseminated. I'd say that it is, thus far, an acceptable price for the vast amount of privilege one has in all sorts of other areas."

The fact is that he's never really stopped, and his most fallow years would be times of hyperactivity for most in his trade. Last year he was playing Henning von Tresckow opposite Tom Cruise in Valkyrie, Bryan Singer's film about the plot to assassinate Hitler; he also directed Michael Caine and Jude Law in a new version of Sleuth.

The year before that he made the hugely ambitious screen version of Mozart's opera The Magic Flute. There was his As You Like It, his portrayal of Franklin Roosevelt in Warm Springs, his directing of the West End hit The Play What I Wrote; Professor Lockhart in the 2002 Harry Potter film Chamber of Secrets; Ernest Shackleton in the Charles Sturridge film of his life for Channel 4. It's a work rate that can be traced back to within six weeks of his leaving RADA and landing a part in Julian Mitchell's Another Country, the play that also launched the careers of his contemporaries Rupert Everett, Daniel Day-Lewis and Colin Firth.

He has even found time to be a stage dramatist, although he seems bashful to the brink of shame when this incarnation comes up. But the plays went on: Tell Me Honestly, a brief satire on organisational life, at the Donmar, and Public Enemy, about his native Northern Ireland, at the Lyric Hammersmith. "Well," he says, "they were good learning experiences. I'd done Fortunes of War on TV, and I had £25,000, quite a lot of money [in 1987], and I put it all into this show. We lost it all. The director, Peter James, said: ‘Isn't it fascinating - no one's coming'."

James told him that he should apply the lessons he'd learnt by staging the show and go away and write it again. "And I thought: ‘Oh my God, he's right. So this is what writing's all about...' They're all linked, the supposedly different skills of writing, acting and directing; all part of what people do in the theatre most of the time, even if they don't do it officially."

Branagh has wanted to do Ivanov for a while. It has come about now, in a version by Tom Stoppard, because of Grandage's shared enthusiasm. The two have been friends since he directed Branagh as Richard III in Sheffield six years ago. From his description, Stoppard has become a little like Chekhov's representative on earth, "or at least a very legitimate voice who can, if he wants, turn round and question him with great authority".

Branagh concedes that spending the days with Grandage and Stoppard is as daunting as it is rewarding. "There is a rigorous examination of every beat of the play. That's exciting, but, Christ, you have to be at the top of your game because these boys are so quick, so bright, such hard workers. They are, as it were, always up earlier than you in the morning."

The play was an early one and is generally seen as a poor relative of the four classics of Chekhov's too brief maturity. But it has acquired striking topicality on two counts. First, it deals with debt, and with relationships dominated by economic circumstance. Debtor and creditor are unable to engage in social or emotional transactions without the paralysing effects of unreturned money. This is credit-crunch Chekhov.

Second, it is set in a Russia desperate to settle and assert its identity in a shifting world order. Chekhov, Branagh says, was at great pains to convince his publisher, Alexei Suvorin, that the play was not about a scoundrel but a despondent man who could and should be understood - "the kind of proto-communist Russian trying to enact benevolent liberalism, which is the step between emancipation and whatever other development of the system for peasants there may be. There they are, in the middle of a nation-changing moment when the fabric of society is being changed, or ripped apart, and men get tired because they are taking too much on."

Type-casting? Not yet. Not for a while.

Ivanov is at Wyndham's Theatre, London WC2 (0870 0606624; www.donmarwarehouse.com)