As the conspiracy geek's preferred pin-up, she was a global star at 24. But, after 10 years on The X Files, she was aching to return to normality... Now, with a nomination for her incandescent performance in Bleak House at tonight's Baftas, that's hardly likely. Here, Gillian Anderson shares dessert and divorce stories with Harriet Lane.

Will she, won't she? I'm half-expecting Gillian Anderson not to show. Two days before we meet for lunch her lawyers released a statement confirming that, after 16 months, her second marriage is over. In her shoes, I'd probably decide that lunch in a Notting Hill restaurant with wrapround plate-glass windows - let alone with a journalist - wouldn't be that high on my list of priorities.

Five minutes tick by; 10, 20. Then the door is opening and a tiny person in big sunglasses is hurrying up to the table and saying hullo. 'Is it OK if we sit over here?' she asks and, without waiting for an answer, bears the bottle of water away to a table in a distant, less populated corner. Off come the sunnies, the ethnic-y pink scarf, the puffy North Face jacket; up goes the menu.

Scanning it in a businesslike fashion, Anderson tells me that the duck salad is very good. Before that, as an aperitif, she'd like a pot of Harmony tea (this is Notting Hill, remember, and she has lived here for several years). With a flash of melancholy humour, she observes that a bit of extra Harmony might come in useful.

I wasn't going to mention the separation until the very end, in case she lamped me or did a runner, but after this it seems rude not to say that you're, you know, sorry. 'Yeah, it's, um, a very challenging and unfortunate time... But on the whole we're both trying to handle it as respectfully and as maturely as possible. It doesn't have to be that way, and at every step there's the worry, "Oh my God, is this going to become a nightmare?" Fortunately, neither of us have any intention of this going on for a long time.'

She says that 'it's really important to know who your friends are at this time. This is when you find out who people really are. And it's sad, really, but it's very educational right now.'

She married Julian Ozanne - who was the FT's Africa bureau chief and is now a financial consultant and a director of a biofuels company - in Hawaii in December 2004. Gossip has had the pair splitting for a while; she put out the lawyers' statement in the hope that 'it might change the dynamic if people just knew it, outright'. In the expectation that you might be able to take back some control? 'One hopes so.' Anderson hails a waiter, asks if she's allowed to smoke in here. No, she's not. 'I don't know why, I'm dying for a cigarette.'

Gillian Anderson is 37. Her parents left the US and moved to London when she was two: her father studied here before starting his own film post-production company. When she was 11, they took her back to Grand Rapids, Michigan, a relocation she resented hugely. (Though she talks about things being 'challenging' and having 'a negative impact', her accent, with me at least, is crisp, unadulterated RP.)

After drama school she became very, very famous at 24 when she landed the role of the sceptical Dana Scully - the geeks' top hottie - in The X Files, a horror/sci-fi series with a higher than usual quotient of literally outlandish conspiracy theories. In the second series, by then married to crew member Clyde Klotz, her pregnancy was camouflaged by an alien abduction (with pleasing symmetry, by the ninth and final series, Scully was herself the mother of a child with supernatural powers). Ten days after giving birth to their daughter, Piper, now 11, she was back on set.

For almost a decade, she and her co-star David Duchovny, with whom she was reported to have a testy relationship, worked 16-hour days, five and a half days a week, nine months a year. Only after the series ended did she realise how unhappy this had made her. 'Not at the time. I had no frame of reference.' She does remember feeling very low during her pregnancy (she started having panic attacks at this time), and after her daughter's birth, and when Piper started reaching first for the nanny.

'You know, early twenties, all the emotions, and I had a baby, and then a divorce, and I was on a brand-new series that was doing well, and all the publicity surrounding that, all the nonsense about David and I, and there were times when it was unbearable.' Hastily, humbly, she adds, 'And yet, I was so fortunate to be a part of something that was so exceptional. We did have fun.'

The panic attacks are still part of her life. In her case, they are strongly associated with the fear of forgetting her lines, an anxiety that peaks when she's on stage. In 2004, in the second preview of a wanly received Royal Court production, Anderson felt the dead weight drop.

'When it happened, I thought: "Fuck, this is the end." All you can think of is, "When can I leave the stage?"' Somehow she got through the show and then, with the director, worked out a few coping strategies, and - touch wood - she hasn't had another attack since then. But she does not tempt fate: 'It's like, if you're dealing with a rattlesnake, the only way to be able to continue is to always remember it's a rattlesnake.

If you forget, you're dead. There's a certain amount of fearful respect that has to go into acknowledging the potential of panic attacks in your life. I bow down to them. Please, not today.'

She seems to have had it with theatre. 'Usually when I do a play - and this is why I don't do them very often - you start rehearsals, it's all great fun, then you get halfway through and you think, "What the hell have I agreed to do, it's too hard, too stressful." And then you get over that and it's fine, and then you absolutely love it for a couple of weeks, and then you start thinking, "Oh my God, is this ever going to end?" and then you realise it's not going to end and you have to make the best of every night. And then you start to learn again, and you do that for a little while, and then you go back to thinking, "When will this fucking be over?" and then you get to the place where you're like, "Oh my God, it's going to be over soon, and this is such a wonderful experience!"' She forks in some duck salad. 'I'm never satisfied. That's part of me, part of my make-up.'

She's not sure where it comes from. It's not a bad thing; she's always pushing herself. 'But on the other hand...'

She stops. I don't get the sense that she is weighing up her words carefully, anticipating everything that might be read into them; rather, she's just trying to work out how best to express the thought that's in her head.

'I do try, very hard, to be happy where I am, I work extra-hard at it, but it's difficult for me, because what is around me is not enough.' Four years ago, she went through a really good stage, she was 'really, really happy', and there's a long, dreamy pause while she drifts off, remembering this happy time, and then she comes to and says, briskly, 'Yeah, but I was doing loads of yoga and meditation. I was going to say I was eating wholefoods a lot, but I think I was living off frozen yogurt.'

She's a funny creature, Gillian Anderson. I warm to her for various reasons. She's got a nice line in non sequiturs. She's un-grand. She's wearing an eccentric pair of white patent leather heels, a tatty old pair of combat trousers and a violet jersey. She swears brilliantly. She gets excited when a waiter carries a tray of puddings past, and races off to feed the parking meter so she can have the lemon tart brulee ('and please get the sticky toffee pudding'). She doesn't have a watch. She's capable, even on a day like today, of moments of almost painful candour. Last but not least, I like her because when the interview is over, she will say goodbye and attempt to leave the restaurant not through the door, but through one of the plate-glass windows. She is, I think, not altogether cool.

Considering she has such a fine line in corseted women whose lives depend absolutely on discretion and steely self-discipline (Bleak House's Lady Dedlock, a wonderfully nuanced performance for which she is deservedly up for a Bafta; Lily Bart in The House of Mirth), it's all the more interesting that Anderson is so impulsive, so open. Having taken a shine to a Starbucks barrista who was sweet to Piper, she hired her on the spot as a nanny (the girl turned out to be fantastic). Clearly, Anderson likes risk. Los Angeles, for instance, was too obvious. The crunch came after The X Files ended, when she found herself on Hollywood Squares, thinking: 'How did I agree to do this? Yes, it's for charity, yes, there's Gloria Steinem, but I feel sick to my stomach, what the fuck am I doing?' So in 2002 she left, and found herself back in London.

It's not necessarily the most sensible place to live if you want to stoke up a career in the movies. 'I don't show my face [in LA] very much, and so that makes it a bit more complicated for me in terms of work. They [producers] need to see you in the press, and in their face, in meetings, auditions, whatever. And as far as they're concerned, I haven't provided enough of an example of the kind of things that I can do, as an actor, for them to justify hiring me without me sitting down in front of them or having me dance around.'

She thinks that's fair enough. Occasionally, she'll fly over for a week, but says, 'I'm not going to go while my daughter's in school here, in the hopes that somebody might take a meeting with me. I'm perfectly happy with it happening slow.' So she makes the occasional foray into quality telly and otherwise pops up in smallish independent films (The Mighty Celt came out last year; Straightheads and The Last King of Scotland are yet to be released). Whichever way, she finds it hard to watch the finished result.

'I don't usually like seeing things I'm in. I get really depressed afterwards.' After The X Files, which sounds as collaborative as it was gruelling, she has found it hard to accept her powerlessness: you have control for a few minutes when you're in front of the cameras, and then the authority passes to someone in the cutting room. 'And I need to forget about that, because that can drive you insane. But sometimes I just can't believe there's certain footage they don't have, even though it seems so obvious.'

And, um, do the directors sense your disappointment? She laughs. 'I try and be very careful, but at the same time I'm very honest. If you ask my opinion, I'm going to tell you that such and such could have been better, or I liked this but I wasn't crazy about that.' Making eyes at my pudding, she wonders if I'd like to try a bit of her lemon tart. We swap plates.

In between acting, she's working on a screenplay which she hopes, one day, to direct: she optioned a novel by Elizabeth Rosner a while back, but now she seems to be struggling a bit: 'It just needs some small things that are, um, major,' she admits, with a little laugh. Her chief recreation is 'buying houses, doing them up, selling them up for a little bit more. Structurally, working with architects, interiors, I love that stuff. I've done it a lot. Twice in London, twice in Canada, twice in California.' Ah, that dissatisfied impulse again. I'll bet she's already starting to think about the sale of the marital home around the corner, and the next purchase.

She describes her current house as 'big and open and white. My... [there's a long pause, while she works out the correct term] husband liked white walls. I like white walls, too. A mixture of funky but mostly standard elements, contemporary, but classic. Then the one before that, off Portobello Road, I just went mad with colour. Spent an exorbitant amount of money on layers and layers of paint. Very funky, bohemian, Moroccan. One before that, in Canada, lots of wood and glass, looking out at the ocean, very grounding.' An eternal cycle of reinvention.

But she and Piper will remain in London? 'Yeah. For now. And maybe we'll be here in 20 years. Or maybe I'll fall in love with Spain. Or India. Who knows? Things are all changing right now. This is really good,' she says, jabbing at the plate with her spoon. 'It's really hard to stop eating. Will you finish it off when I've left?'

The meter's about to run out again. She has to go to the wholefood shop, Fresh and Wild, and then collect Piper from school. I can't sit here on my own, troughing through a pudding, I say.

'Yes, you can. Please don't write that I scoffed two desserts. You can be honest about it and say that I ate all of mine and half of yours. Well, I'm going to have one more bite before I go.'

I say I'm surprised she didn't cancel. No, she says, it never crossed her mind. 'No. I show up. That's one thing I do.'