Having tea with Gillian Anderson is a thoroughly pleasant business — a splash of muted glamour in a fairly drab London autumn. I thoroughly recommend it, as a more engaging companion it would be a challenge to find.

We meet in the studiously bijou surroundings of the Zetter Townhouse in St John’s Square, chosen, I suspect, because no one there has the slightest clue who she is. She is wearing the no-make-up disguise, and glides serenely under London’s radar, something she clearly enjoys. She is a tad jetlagged, she says, having just arrived home from a three-week stint ‘doing press’ in LA.

We are talking in the Games Room downstairs when there is an unexpected rattling at the window. We are momentarily flustered – is it a stalker?, a pap? — though all is well and we laugh off our over-reaction. In that moment, though, when we glare at one another wondering if we should be alarmed, I see those green eyes and Special Agent Dana Scully appears before me.

It isn’t long before Gillian returns, but I am reminded of that time and look more closely into her face. The camera loves Anderson: as the cult star of the biggest cult series on TV, she was one of the faces of the Nineties.

‘It feels like another world,’ she says, when I ask her how that felt. ‘Well, it was a lifetime ago. But more than that, that life, that in the public eye, top of the list, all that feels like it happened to someone else. Thank God I was so young, and strong, and naïve — I certainly couldn’t do it now, I wouldn’t be able to cope with it at all. I was lucky that we shot the first five series of The X-Files in Canada, so we were far removed from the sensation we were creating. I spent those years learning how to act, playing Dana Scully — I didn’t have time for the rest of it, though I remember being overwhelmed by it when I was back in LA between filming.’

And being voted the sexiest woman in the world? Gillian waves this away in the most dismissive manner possible. Weird? ‘Absurd.’

It’s all different now: low-key and local in London, where she has lived since 2004. ‘Yes. The madness of how my life was then makes me very, very grateful that I don’t have paparazzi outside my door. I mean I’m pretty private, and I enjoy my privacy.’

‘And of course I love it here,’ she tells me. ‘London is my favourite city in the world. Flying in last night, I felt I was really coming home, and that’s unique. It’s the only place I actually miss when I’m not here. London appeals to many aspects of me — it just feels like where I belong. And it’s a great city to bring up children.’ (She has two young sons and a teenage daughter.)

Anderson not only lives in London, but works here too. She played Lady Dedlock in the 2005 BBC adaptation of Bleak House, winning nominations for just about everything, and recently appeared as Wallis Simpson in Any Human Heart (Channel 4, Bafta), alongside ‘my friend’ Tom Hollander and the ‘unimaginably sweet’ Matthew Macfadyen. She moves with ease between an American and English accent, having lived in London as a child, and is cornering the market in female characters of a certain age.

Anderson plays the ‘M’ part — MI7 Secret Agent Pamela Head — in the recently released Johnny English Reborn, Rowan Atkinson’s second spoof Bond film. ‘That was great fun. Rowan is a bit of a genius, so it was fascinating watching him at work — how specific he is; he’s quite a curious character. And the film is very funny.’

Then, on the horizon, there is the coveted role of Miss Havisham in a BBC adaptation of Great Expectations, to be broadcast over Christmas as an early celebration of the Dickens bicentenary in 2012. The Daily Mail describes it as ‘sexed up’.

‘I wonder where that came from, it certainly doesn’t have anything to do with me,’ Anderson says. ‘Sexually charged’ was the quote — maybe coming from a BBC controller describing Sarah Phelps’s screenplay as a ‘visceral re-telling’ of the Dickens classic.

‘Well, it’s an absolutely cracking cast and certainly I think that you realise early on the weight of something you’re involved with,’ Anderson says. ‘As also happened with Bleak House, I knew I was working on something very special.’ Both she and Ray Winstone, playing Magwitch, are younger than those characters have been played in the past.

‘That’s true, and maybe that’s part of what the BBC were trying to get across, a kind of Mrs Robinson thing. But what’s interesting is that I took my lead on that from Dickens. When Pip first goes to Satis House, Dickens tells us that it is only 15 years on from when Miss Havisham was abandoned at the altar. So she could be, potentially, as young as 35. I play her as my age [no, I don’t ask, but it’s early forties], but with silver-grey hair — as far as I’m concerned she went grey overnight from the shock of the jilting. How that plays out visually with the ­disintegration of Satis House is awesome.’

Gillian is preparing to leave for a spot of filming later this afternoon when a fire alarm goes off in Zetter Townhouse and, though we were politely warned in advance, we both jump a foot out of our chairs. ‘Whatever next?’

I ask about parts she would like to play and she answers without hesitation: Blanche DuDois — ‘before I get too old’. She is currently in negotiations with a ‘very big theatre in New York’ for what would be her Broadway debut, but she doesn’t say if Streetcar is the production. ‘I love theatre, but there’s a kicker to that, which is that I get very, very nervous. I have panic attacks. It’s horrendous and I had it pretty badly with A Doll’s House [Donmar, 2009]. I have to block that out completely because if I didn’t I’d say to any theatre project: “No way, I can’t ever do that again”.’

As Anderson rises to go, I ask her if living in London reflects her preference for outsider status. ‘I’m not sure. I think that certain aspects of your personality, when you’re younger, feel like a choice, but when you get older those same character traits have ingrained themselves, you get used to them and then they just suit you.’

She can’t find her way out, and it feels like the Games Room is playing its last trick on us. There is nothing flamboyant or spectacular about the former X-Files star, but she is mesmerising in a way that is difficult to describe; she appears unaware of it herself. Maybe it’s only the camera that really gets it.