Gina McKee's trademark is cool detachment, so why is she blushing on the inside?

And so, with mixed feelings, to meet Gina McKee, the long, slim, murmuring Geordie actress with the Modigliani looks and the Sphinxlike demeanour. On the one hand I’m intrigued to meet this elegant enigma in the (alabaster) flesh, who has stealthily become one of the most respected performers of her generation. On the other hand I have read enough press cuttings to note the repeated use of phrases such as “evasive civility”, “details seem slippery” and “famously tight-lipped about her personal life” to fear that all I will return with will be long, dutiful passages about her work.

I needn't have worried. For a start she seems relaxed – almost chatty – on the afternoon that I meet her, draped over a sofa on a top-floor room of a London restaurant. Casually dressed in T-shirt and black jeans, she is fresh from adding ADR (additional dialogue recording) to her part as an investigative journalist in Channel 4's new conspiracy thriller, Secret State, a remake of their 1988 series, A Very British Coup – of which more later.

Although there is an inner core of her personal life that remains off-limits – that's to say her relationship with her husband of 23 years, Kez Cary – she doesn't seem particularly evasive about the rest of it. Perhaps it's just easy to mistake slowly measured thought for evasion. We break the ice with a discussion about my digital recorder. "Oh, I have this exact same microphone… use it for learning lines," she says. It seems McKee records the other actors' words, with suitable gaps for her own lines. "It means you don't bother people saying, 'Can you help me with this?', which drives people nuts. Anyway, that's exceptionally dull… you didn't need to know that."

Not at all, and anyway this self-reliance becomes a recurring, underlying theme of her story. First up, however, I congratulate her on her performance as the mother in the BBC2 sitcom Hebburn. She plays a Tyneside housewife married to Vic Reeves – or rather Jim Moir, as he calls himself when he's not being Vic Reeves – and McKee seems wonderfully skittish and liberated after so many anguished roles (the wife of a man arrested for downloading child pornography in Fiona's Story, the mother covering up her son's crime in The Street, the wife whose family is swept away in Tsunami: the Aftermath, Kenneth Branagh's terminally ill wife in the Donmar production of Chekhov's Ivanov… I could go on).

"Three years ago we did In the Loop [the Armando Iannucci satire] and I really enjoyed it," she says. "It was a real shot in the arm. I kept saying, 'I've got to do some comedy, I've got to do some comedy'… and then when I knew Jim was cast… I've been a huge fan of Vic and Bob… so I was very excited about that. And a little bit nervous, actually. I rarely get nervous about meeting people and sometimes it's unexpected."

Unexpected indeed, given the calibre of some of the talent she's worked with over the years, including Hugh Grant in the Ken Russell phantasmagoria, The Lair of the White Worm, Christopher Eccleston and Daniel (or "Danny", as she calls him) Craig in the Nineties TV classic Our Friends in the North, Homeland star Damian Lewis in The Forsyte Saga, Clive Owen in Mike Hodges' Croupier and, of course, Julia Roberts – McKee playing the wheelchair-bound Bella in the 1999 Richard Curtis rom-com Notting Hill.

"The first day we met for a rehearsal, I gave myself a little talking to: 'Don't get nervous…'," she recalls. "And when I got in there Julia and I were wearing the exact same pair of trousers and for some silly reason I was embarrassed she would think I was trying to copy her – so I didn't take my coat off all day. Anyway, it's completely unnecessary – she's very easy to be with and wants to do her job like everyone else."

The global success of Notting Hill got McKee an American agent, and roles in films with the likes of Willem Dafoe and Sandra Bullock – and it still wins her jobs today, some 13 years later. "I recently did a film with a French director – it was a straight offer I didn't have to meet for or audition, which is fairly unusual. The director [Arnaud Desplechin] was struggling to cast this English character – he kept saying 'no' and finally the US casting director showed him these scenes from Notting Hill and he said 'yes'."

The film is Jimmy Picard, the true tale of a Native American ex-serviceman, and her co-stars are Benicio del Toro (Usual Suspects, Che) and Mathieu Amalric (Quantum of Solace, The Diving Bell and the Butterfly). It's a very long, exotic way from McKee's upbringing in County Durham, in the "classic post-war new town" of Peterlee, where Georgina McKee was born in April 1964, her father working in the nearby Easington Colliery.

"A distant cousin sent me some genealogy report on my father's side, and it's sort of what I suspected," she says. "Coal miners for generations… four or maybe five generations. Easington Colliery is just a landscaped field now, with a ventilation shaft – I guess for the gasesf – and a small commemorative garden with the wheel. It's quite a contrast to how it was." How does she feel about that? "I don't know entirely. I think if I lived there I would have processed how I feel about it more. I don't know fully what the community's like now."

In fact, McKee rarely returns since the death of her parents. Her father took early retirement after the 1984 miners' strike, and McKee's brother had to move away to find work, becoming (ironically given the turbulent times, and McKee practically whispers the fact) a policeman in the Metropolitan Police. By the time of Arthur Scargill's last stand against the Thatcher government, however, McKee was 300 miles away in London, a jobbing actress with that most precious of commodities back in the day – a union card from Equity.

How did the coal miner's daughter get to this point, especially, as she says, "the environment we were living in was not one of the theatre or the arts"? By way of a succession of inspiring individuals, it would seem, starting with her primary school teacher, Mrs Hall, who introduced her pupils to improvisation. "Of course it was never described as that, but it was bringing the playground into the classroom," says McKee. "I loved it, but of course it was never seen as something that could be useful in your life."

At secondary school, McKee read a "hand-written photocopied A4 sheet of paper" (the memory is obviously firmly imprinted) on a shoe-shop window, advertising a teenage drama workshop run by Ros Rigby (now an OBE, and a director at the Sage, Gatehead) and her husband Graeme Rigby of Amber Films. McKee and her friends went along for af laugh, except that McKee was "hooked… although I didn't admit it".

One of their productions was watched by someone from the local ITV station, Tyne Tees, which led to a job in a children's series, Quest of Eagles.

In the meantime, she spent three summers from the age of 15 in London (being put up by the relatives of one of her teachers) attending the National Youth Theatre. At 17, she applied for and was rejected by three drama schools, but by then she had something almost more valuable than a Rada education. She had an Equity card from her stint on Quest of Eagles.

"Back then it was a closed shop, and I was in a fairly unique position of being a young person with a provisional Equity card," says McKee. "I got offered a few jobs, and kept going and kept going." Not that she skimped on her education. "I would go off and do classes because I needed to know skills you would learn in drama school, and I needed to make sure I wasn't lacking. City Lit [the City Literature Institute in London] is particularly good. I would go regularly because it was affordable." She's self-taught then? "Self-motivated, maybe… yeah."

Work remained steady and varied – with supporting parts in the Mike Leigh film Naked and in TV shows such as Inspector Morse, The Lenny Henry Show, Drop the Dead Donkey and Auf Wiedersehen, Pet – but unspectacular. And then in 1995, at the age of 31, she was cast as Mary Soulsby in Peter Flannery's time-lapse drama Our Friends in the North, alongside Christopher Eccleston and the then unknown Daniel Craig and Mark Strong.

"I was very lucky, wasn't I?" says McKee. "I remember loving the scripts and then having that bittersweet feeling where every fibre of your being says, 'I want to do this, and it may not be yours'."

Flannery's drama followed the mixed fortunes of a group of four friends from Newcastle from 1964 until 1995, by which time McKee's character, Mary, had become a Labour MP, a proto 'Blair's Babe'. "All the boys were cast and I wasn't and I remember having to go for a screen test with Mark and they gave us a scene where they're lying in bed together and they had us lie on two tables that they'd pushed together. And I think they had concerns about what I would look like in Sixties make-up, so I was given a nylon, black, long wig and very heavy Sixties eye make-up. I looked like a drag act trying to be Cher."

Despite the look, McKee won the role, ageing from 18 to 52 on screen and winning a Bafta. Was it career-changing? "Markedly but not immediately," she says, after her usual consideration. McKee is not one to jump into answers. "In fact, I was unemployed for a while after I won the Bafta. But there was a definite change… better roles… more interesting things to do."

One of those things was playing the vampy news reporter Libby Shuss in Chris Morris's Brass Eye, displaying the comedy chops that have resurfaced in Hebburn. She seems particularly pleased when I mention that The Independent's TV reviewer had, that morning, heaped praise on the show. "I'm going a bit red… I'm burning up now… I don't know why," she says. "You don't go red," I say, looking closely at her still resolutely alabaster cheeks. "No, you haven't gone red," confirms the PR. "I don't know if I'm physically going red," says McKee, "but I'm feeling really hot."

Part of McKee's pallor might be to do with her low blood pressure ("All the doctors refer to it"), partially the result of not eating meat since 1982. "I was one of those kids who found it difficult to eat anything that looked like an animal," she says. "If you were given a leg of turkey at Christmas I would look at it and think 'It's a leg'." Movie location catering can prove a problem, especially abroad. "I did a film in France where they actually went 'Phfah!' when I asked them for vegetarian food and served me a fried egg one day on mashed potato."

Her slimness could also be attributed to her devotion to walking. Seven years ago, she and husband Kez moved from north London to a village in East Sussex ("to try a different rhythm"), choosing a house with the South Downs on their doorstep. "We can just step out and go for a hike. I still get a fix of London, because I do love London and I'm here for work a lot. And travelling to different places is always a joy for me. But I do love going back… it's so good."

She doesn't have any children. Dogs? "No, none of that." Anything else she would like to tell me about her personal life? How does she unwind? "Being at home with my partner… eating well… as simple as that." Her partner? "Husband… I'm not going to go into it. He was in the industry, but not now."

Perhaps if McKee doesn't talk about her personal life, one reason might be that it isn't particularly fascinating – by which I mean, it seems ordered, settled and contented. It probably needs to be because her work, by contrast, seems endlessly varied. Currently she is filming her on-going role as the warrior Caterina Sforza in The Borgias, while finishing dubbing Secret State.

A remake – or rethink – of the 1988 series A Very British Coup, which, in turn was adapted from Labour MP Chris Mullin's novel (Mullin has a cameo in the new series, as a vicar), the Channel 4 drama series stars Gabriel Byrne as the deputy prime minister eased into 10 Downing Street after the death of the PM in a plane crash. McKee plays an investigative reporter being fed leaks damaging to the petro-chemical industry. Sounds dangerous – does she survive all four episodes? "How many have you seen?" she asks, with a glint in her eye. "Only one? Then I'm not going to tell you."

'Secret State' begins on Channel 4 on 7 November; 'Hebburn' continues on Thursdays on BBC2