The last time I saw the 28-year-old actress Jodhi May she was a right sight. Dressed in a dirty slip in the opening scenes of Christopher Hampton’s The Talking Cure at the National, she twisted and twitched in sweaty orgasmic convulsions as the mental patient Sabina. But the next time she appears on stage she’ll be a vision in white: the spirited Nina in Chekhov’s The Seagull, directed by the German theatre legend Peter Stein in Edinburgh.

May is tall, warm and loves a “challenge” — one of her favourite words. “What fires me up is if I think this is really going to be very hard, very difficult, and it’s going to push me into areas where I feel very out of my depth.” She says that Stein is very rigorous and a hard taskmaster, which she finds both challenging and exhilarating. Over an austere meal during a break from rehearsals, May, a dark beauty, comes across as thoughtful.

When she sees I’ve got a book about Chekhov, she immediately makes a note of the title.

“Peter comes from a European tradition, so he’s incredibly involved in your acting,” she says. “The British tradition is to maintain a distance between director and actor, but Peter is very passionate. Europeans don’t tiptoe around you, they don’t find a polite way of saying things. He’s a really hands-on director.” I get an image of 66-year-old Stein manhandling the cast. Do the actors ever tease him? “No, because although he seems very serious, which he is, he also has the most fantastic sense of humour. He mocks himself; he’s self-deprecating. People fall in love with that quality. He’s not precious — he loathes pretension. And he’s very gutsy,” says May. “Lots of people describe him as old-fashioned, but to me it seems absurd that being completely dedicated to the author’s intentions and the text should be seen as old-fashioned.”

In fact, you get the impression that May is similarly old-fashioned. She’s serious with a capital S. She sees Nina as someone not vapid, but incredibly bold in choosing the stage: “Fiona Shaw’s mother, Arkadina lent me a biography of the actress Eleonora Duse, which gave me an insight into the psychology of someone who made that choice to become an actress at a time when it was like becoming a prostitute.” As she talks, May drops in bookish words such as “objectifying”, “projection” and “juxtaposition”. Then comes a flash of insight: “I think Nina is the most alone of Chekhov’s characters.” She believes that Nina is fas-cinated by the world of intellectual interchange, which is for her emotionally enriching — especially when she’s had a father who has been neglectful. Symbolised by the seagull, Nina is someone of great independence and flight, but that’s about liberation and freedom, not sentimentality, according to May. “Chekhov was interested in darkness — someone whose soul is taken from them — and not in sentimentality,” she says.

There’s a risk that May’s own life might be sentimentalised. Born in London, she was an only child brought up by a single parent, her mother. She liked painting and took drama lessons after school. Spotted by a casting agent, she won the best actress award at Cannes for playing Molly, the daughter of anti-apartheid activists in the 1988 film A World Apart. She was only 12 years old. She started as she’s carried on — by doing in-depth research. “For three months, we went to live in Bulawayo, Zimbabwe, where the film was shot. The place had almost not changed since the 1950s, when the film is set. I lived with a South African family and went to school, which helped me pick up the accent.” Her role model was the film’s star, Barbara Hershey, a very serious woman.

I ask about her mother and father, but May slaps me down: “When you’re acting you have to be involved with the press, but your parents don’t have that choice, so I think it’s important to protect them.” Her mother is an art teacher, and French. When May was a child, her mother introduced her to Truffaut films and took her around art galleries. “As an only child, you’re more likely to be drawn to what your parents like,” says May. She also read a lot.

“I don’t feel strictly English,” she smiles. “I do identify much more with Continental Europe. Growing up in England I was a bit of an outsider culturally.” When I ask her if she wanted to be English when she was little, she suddenly becomes passionate: “Oh my God, desperately. Absolutely, absurdly so! In a way I now think I desperately don’t want to be.”

Her career has featured serious, lonesome heroines. In The Last of the Mohicans, she threw herself off a cliff; in the telly drama Signs and Wonders, she ran off to join a religious cult; in The Woodlanders, she pined for love; and she’s slipped into corsets again and again in dramas such as The Aristocrats, Tipping the Velvet and Daniel Deronda. She talks knowledgeably about Victorian sexuality and “the hysteria-isation of women”. But when I mention feminism, she wrinkles her nose.

In 1994, she went to Wadham College, Oxford, to study English, as an antidote to the stress of filming. Inspired by teachers at Camden School for Girls, she fell in love with literature when one introduced her to James Joyce’s A Portrait of the Artist as a Young Man. She liked Oxford because “working on a text is just what actors do, so it was good practice”.

May worries about the narcissism of celebrity: “For me, the process of acting is rewarding, but I think it’s dangerous if you set too much store by what other people think.” Don’t expect to see her falling out of a dress at a film premiere or in Hello! magazine. Once asked whether she’d like to do a sitcom, her answer was “definitely and absolutely not”. She doesn’t even have a television, so there’s no point asking her about Big Brother or EastEnders. Her desire is to be anonymous. “What intrigues me is the idea of disappearing into parts,” she says. “I like adopting roles in such a way that you as an actor disappear. It might sound terribly wet, but all the actors I admire have a humility and they are actually devoted to what they do.”

Recently, May starred in a French-language version of Caryl Churchill’s Far Away, directed by Peter Brook in Paris. “I’d love to feel relaxed and complacent,” she says. “But I don’t feel a sense of having arrived. When you work with people like Peter Brook, you feel as if you’re starting from scratch. He takes you to a place where you feel terribly vulnerable. You have to just go with that.”

When actors play actors, there’s always a feeling of empathy. By the end of The Seagull, says May, “Nina’s child has died, but it’s almost as if she’s actually saying, you know, what was so terrible about that was that it really affected my acting”. She gives a grim but gutsy laugh. She knows what it takes to slave for your art. As I take my leave and step into a gusty Edinburgh afternoon, I look up and see a circling seagull — a good omen, surely.

The Seagull is at the King’s Theatre, Edinburgh, from Aug 11