Patrick Stewart strolls over to our table at a Stratford restaurant in a loose grey linen jacket, ducking slightly under low beams. Tall and lean, with his bald head and pointy ears, he looks a bit like a very grand satyr. He has come straight from rehearsals for Hamlet, in which he plays Claudius opposite David Tennant's Hamlet, and delivers a top-value performance as a lunch companion, telling stories with dramatic brio in his trademark master-and-commander, basso profundo voice.

When I mention that I saw my first Hamlet on a school trip with David Warner in the title role, he sighs deeply. “You saw the Hamlet of my generation,” he says reverently. “I remember leaving the theatre shaking with excitement; I'd never seen Shakespeare like this, so natural, so thrilling.” Six weeks later, the 26-year-old Stewart joined the RSC: “And I could watch it all at close quarters and learn.”

Forty years on, Stewart is playing both Claudius and the ghost of Hamlet's father. It was his idea: “They are brothers so it's natural they would share some genetic similarities: body language, voice, certain expressions...” How is he doing Claudius - lustful and evil? “You mean typecasting?” he quips. “No, it's a love story; Shakespeare gives you plenty of clues to that. Old Hamlet was a distant figure, a warrior, away from home a lot, hero-worshipped by his son. Claudius is a negotiator, a diplomat.” And he gives Gertrude the attention she didn't get from Hamlet's father? Yes, exactly.”

By his own account, Stewart himself was more like old Hamlet, at least in his first marriage, obsessed with work, a largely absent father. “God yes, even when I was there, I wasn't there. My son Daniel, who is also an actor, gave a speech recently in which he recalled as a child being told often by his mother: ‘Shh, your father is learning his lines.'” Does Daniel resent his father's remoteness when he was growing up? “Doesn't seem to, no,” Stewart says, comfortably. “But as a father he is taking a very different attitude to me: for him family comes first.” To the extent of turning down work? “Oh yes, in fact he's just done exactly that.” And you never did? “No, never. It was only work for me. I was so much in love with it.”

Until 15 months ago he was with the actress Lisa Dillon, 29 years his junior, and he has just started another relationship with an American woman, also much younger than him. Stewart was 68 this month. What does he feel about ageing? “Well I'm afraid of dying, yes, you can tick that box, and I work hard on fitness.” He has a gym at home and power-walks. “If you want to be a classical actor, as Laurence Olivier said, you have to be fit as an athlete. You can't go around with a big belly hanging out, drinking late at night.”

Does he have younger girlfriends to keep him young? “No, it's not that,” he says. “I don't search them out. I just don't meet women of my age.” He assures me that he is not being disingenuous. “I won't have more children,” he says. “I have four grandchildren who I adore - my family is complete.”

Stewart recently finished a 17-week run as Macbeth. “I had three days off before starting Hamlet,” he says. “I walked into the rehearsal room and thought, my God this is exciting: I'm with all these brilliant, talented people and I'm about to open the script of possibly the greatest play ever written. What a way to start your day.”

Daily rehearsals involve a 50-mile round trip to Stratford from his home in the Cotswolds. “I love every minute of it,” he says. “Because of those 17 years away, the English countryside has taken on a significance it didn't have before. I was driving home after work - a soft June night, listening to a classical station - and a Vaughan Williams piece came on...” He stops for a moment, apparently overcome.

Did he cry?

“Yes, I had to pull over. I couldn't see to drive.”

Does he find as he gets older that he is more easily moved?

“God, yes,” he says. “Do you?” I confess that when I came home after 11 years away, I cried all over the place, and he tells me about walking on the South Downs one evening last summer, looking down on a hamlet in a wooded valley, a curl of smoke rising from a single chimney. “I burst into tears,” he says, “All that history and it was still there.” His eyes fill up and mine do too - silly old us, weeping over our fishcakes in an empty restaurant.

He never meant to stay away so long, he says. It was just that Star Trek took on a life of its own. Before landing the role of Captain Jean-Luc Picard, he had notched up numerous TV and film roles, in I, Claudius, Tinker, Tailor, Soldier, Spy and Smiley's People, the film Excalibur and David Lynch's Dune. But it was Star Trek that propelled him into the global limelight - he was so good as Picard, with his bald head and Spocky ears, and he loved doing it. In fact he once said... He stops me: “I know what you're going to say,” he groans. “That quote has haunted me.” What he said was that all his years at the RSC and the National, playing kings, emperors, princes and tragic heroes, had been nothing but preparation for sitting in the captain's chair of the Enterprise. “The fact is,” he explains, “I was fed up with journalists constantly suggesting that I was slumming it. I said it in a sort of weary defiance, but there was some kind of truth in it: Star Trek was very theatrical - a throne, a king - classical in a sense. And the people who did it well all had a background on the stage.”

Still, he was no slouch in those years: on top of starship duties, he formed a production company with his second wife (his first marriage had ended in 1990), developing film and TV projects (“Not a single movie got made - it's a heartbreaking business”); played a dance instructor hitting on rich women in a film that was never released (“It was worth it to twirl down 53rd Street with Lesley Caron”); and created a series of one-man stage shows. The most successful - it went to Broadway and the West End - was a rendering of A Christmas Carol and he consulted a Dickens expert about his editing of the text. “I wanted it to be respected as a piece of scholarship. The language is astonishing,” he says. The deep voice booms into a description of Scrooge: “A tight-fisted hand at the grindstone. A squeezing, wrenching, grasping, scraping, clutching, covetous, old sinner.” He leans back in his chair. “You'd never be allowed to do all those words on television.”

Since leaving Picard behind Stewart has played a succession of big stage roles - his Othello in 1997 was a white man entering a black society; he played Prospero in the RSC's The Tempest in 2006 and the following year appeared as Anthony opposite Harriet Walter's Cleopatra at the Novello Theatre in London. He has also returned to sci-fi as the wheelchair-bound Professor Charles Xavier in the X-Men films.

Raised in West Yorkshire, soldier father, mother a weaver, Stewart went to a secondary modern, struck lucky with imaginative teachers and went on to study drama at the Bristol Old Vic. “My father was born near Jarrow, an instinctive radical,” he says, “and I've been a Labour supporter all my life.” He was in California when John Smith died after a brief time as leader of the Labour Party. “I read his obituary and felt a real connection,” he recalls. “I called the party and joined over the phone.” He felt ashamed, he says: “Here I was living the good life in LA, talking about whether one was going to Hawaii or Malibu...I thought what am I doing? Bugger all. So joining was a sort of political gesture.” Despite the “disaster” of Iraq, he has faith in Labour's future: “I haven't given up on them or on Gordon Brown. He is not doomed, as people say, I don't believe that.”

It is time for him to return to rehearsal. But before he does, I must ask if the story he has told so often is true - that he bunked off school on the day of his 11-plus exam and went walking on the moors. His eyes widen. “Of course it is. I didn't want to go to the grammar school; I would have sunk without trace. It was absolutely the right decision; I flourished at the secondary modern. Look...” He fishes around in a breast pocket and produces a small metal badge with the words “Head Boy” printed on it. “They gave me this badge on Macbeth, but I was actually head boy at school - and a year younger than usual.”

He stands up, pinning the badge on his lapel, shakes hands and then he is gone - no doubt to exercise his head-boy talents on another cast.

Hamlet is at the Courtyard Theatre, Stratford-upon-Avon, July 24-November 15 (www.rsc.org.uk, 0844 8001110)

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