Who's that girl?: Actress Gina Mckee is nothing like the damaged women she portrays

Elegant, alabaster-pale and with a measured murmur of a voice, Gina McKee is, initially at least, regally inscrutable. But every so often you catch a chink in the actress's unruffled exterior. More than once she breaks off from one of her thoughtfully evasive answers to say, with a hefty hint of Geordie, "blether, blether" or "I don't want to sound too poncy..." When I walk into her opulent hotel suite, she is standing looking meditatively out of the window, a vision of LK Bennett-esque grace in a neat purple cardigan, knee-length black silk skirt and ballet pumps, but, as she turns, she crams a biscuit into her mouth and mumbles hello through a mouthful of crumbs. Later, when there is a knock at the door, she leaps up to open it and sprints girlishly down the corridor.

This ability to combine an ethereal star quality with that of a down-to-earth everywoman in her performances, which offer only the mildest of hints at the eddies of emotion swirling beneath a coolly restrained surface, have made McKee one of Britain's most respected actresses. The star of Our Friends in the North and Notting Hill (she played the wheelchair-bound Bella) is now appearing in Tom Stoppard's new version of Ivanov, the inaugural production in the Donmar's West End season. McKee's first Chekhov role pits her opposite Kenneth Branagh and the rapidly rising stars Tom Hiddleston, Andrea Riseborough and Lucy Briers. As the tubercular wife of the philandering Ivanov (Branagh), Anna's physical and mental health disintegrates as her husband indulges in a mid-life crisis. "Somebody asked me at work, 'is this the first Chekhov play you've done?' And I nearly said 'no'. I don't even know why," she admits. You can see why, though. McKee and Chekhov would seem to be a match made in heaven – all wan suffering and overwrought emotions bubbling under the surface.

The role of Anna comes hot on the heels of McKee's last television appearance in the hard-hitting BBC drama Fiona's Story, in which she gave a perfectly reined-in performance as a middle-class mother whose husband is arrested for downloading child pornography. Before that, she played a 1960s housewife indulging in sexy role-play with her husband and an enigmatic woman who may or may not have had an affair in Pinter's The Lover and The Collection in the West End – two more parts that played on her sphinx-like coolness.

So does all this repressed emotion burst out of her when she stops working? "I was filming Mike Leigh's Naked and I was really immersed in it and enjoying the dark territory. I went to a dinner party and one of my friends asked, 'do you not bring it home with you?' I said, 'no' and, at exactly the same time, my husband said 'yes'." She smiles ruefully. As a rule, McKee likes to keep the boundaries strictly drawn between home and work. Of her husband, she says vaguely: "He's been in the industry but he's not now. What's great is that he understands how it works." She's aware that she has previously come across as frostily guarded on personal matters. "There's a way of negotiating how you portray your private life publicly that I've never had the skill to do," she confesses. "In the beginning I was slightly clumsy about it."

McKee grew up in the mining community of Peterlee in County Durham. Far from being a precocious child star, her only early theatrical memory is of Friday afternoons in junior school, when a certain Mrs Hall would get the class to act out stories. As a teenager McKee spotted a poster for a youth drama workshop in a shop window and joined up. She was spotted by a scout for Tyne Tees television and landed a part on the children's show Quest of Eagles in 1979. On leaving school, McKee was all set to study theatre design at art college. "But at the eleventh hour I got on a midnight bus to London." There, she applied to and was rejected by three drama schools – Bristol, Lamda and Central. "To be fair, Central said come back next year, when you're 18. But by the time I was 18, I was working. I think those three schools recognised that I wasn't going to settle down there. Maybe it would have helped. I was a bit on the back foot – I wasn't very good about advertising myself. It was a slow burn."

Slow burn or not, she soon landed parts in Auf Wiedersehen, Pet and Inspector Morse, but it was Peter Flannery's Newcastle epic, Our Friends in the North, adapted for television in 1996 with a cast including Daniel Craig, Christopher Eccleston and Mark Strong, that made McKee's name. "On reflection, that did change things," she says, carefully. It was her big break, wasn't it? "I try to avoid, I don't know, something as definitive as that..." In her Bafta-winning turn as Mary, McKee aged from 18 to 52. Now 44 years old, does ageing concern her? "No. It's great being in your forties. I feel like I've got enough history to learn from and enough future to enjoy."

That said, when I ask her later about one of her credits on the movie website IMDb, she launches into a good-humoured rant. "They've got my age wrong! I'm younger than that. I was born in 1964, not 1961. I don't think I've got anyone else's CV. But I've got somebody else's bloody age. One of my agents tried to change it and they won't – I suppose they think every actress is trying to pretend they're younger..."

Next up, McKee is returning to comedy, which will please those who remember her wicked turn as the vampy newshound Libby Shuss in Brass Eye. She's playing a senior civil servant in In the Loop, a feature-length spin-off of The Thick of It in which the politicos travel to Washington and meet their American counterparts. Having worked with pretty much every significant name in British film – Leigh, Richard Curtis, Michael Winterbottom (Wonderland) and, lately, Joe Wright (Atonement), does she hanker after a Hollywood career, like that of her erstwhile colleague Craig? "I'm chuffed to bits for Danny. But it's not an obvious comparison, is it? I'm never going be James Bond, I've got to face that. But I've never put up geographic boundaries for my work. Plenty of people are going to put things in your way, why would I do that? I'm in a position where I can easily travel. I'm married but I don't have children so it's not like I have to stay for school and all that. But the whole big-time Hollywood thing, it's incredibly unlikely, isn't it?"

Would she feel adrift in LA, away from her Northern roots? McKee thinks hard for a moment before giving a typically ambiguous answer. "Where I grew up in the North-east, the community there, and the way people relate to one another, goes very deep. But I don't define myself as a Northerner in that I don't live in the North. So what does that make me?" she ponders. "I suppose I'm a bit of everything, like a Woolworths pic'n'mix."

'Ivanov' runs at Wyndham's Theatre, London WC2 (0844 482 5120) to 29 November