Gillian Anderson is a woman of many duelling qualities, and it is hard to know quite what to expect when meeting her. Her old interviews are displays of either surprising candour or frosty reserve. She can be earnest and thoughtful, sometimes to the point of seeming grave, yet she peppers her social media with “penis/yoni of the day” posts, pictures of things that happen to look like genitals, even when they are not. She speaks with an American accent when with Americans, and with a crisp British accent with Brits, though she retains a US sheen on only one word that I clocked: “process”. She is extremely famous and has been for more than half her life, yet has maintained a sense of mystery and intrigue, and is keenly private.

Naturally, then, in a photographic studio in a tiny back street in north London, talk has turned to tattoos of Anderson’s face on strangers’ buttocks. It started with one of her own cashmere jumpers, part of her new capsule collection for the London brand Winser (she turned designer for them in 2018, adding another string to an already creaking bow that includes activist and author, as well as actor) that features a familiar-looking mouth emblazoned across the chest, accented by that Monroe-esque beauty spot.

“It is a strange thing, yes,” she agrees, adding that of all the pieces, she probably won’t make a habit of wearing the one with her own face on it. It’s an impish design, but this being Anderson, there’s more to it than a bit of self-reflective fun: some of its profits will go to Women for Women, which helps support female survivors of conflict.

‘The silly side of me has always been there’: Gillian Anderson wears dress by Prada. Photograph: Gustavo Papaleo/The Observer

“Well, the way that started was, a fan showed up with a T-shirt that she had made with my mouth on it. Which I recognised, and I went, ‘Wait, is that…?’” That might be an unnerving experience for most people, but Anderson has to admit that for her, it is not so out of the ordinary. “I’m kind of used to it,” she shrugs. “Especially because of my old job. The enthusiasm of the fans, from being in something that’s remotely science fiction, is more intense. And so I’m used to tattoos on calves and buttocks and stuff like that.”

In 1993, The X Files arrived on television, with Anderson at the helm as the sceptical FBI agent Dana Scully. She had just turned 25, and she found herself at the frenzied frontier of a cultural phenomenon. The tattoos soon followed.

“It was really early on, actually. I had gone to Australia to do press, and somebody had David Duchovny and me on their buttocks, and were offering to show us.” She laughs. The thought of what they might look like now tickles her. “I don’t know whether we are both less… chubby-cheeked?”

Anderson has been wrangling with what is public and private for the past three decades. Recently, she has found herself having to think about it again. The X Files came back in 2016, after 14 years away, and now there is Sex Education, the Netflix teen comedy-drama in which she plays a sex therapist. “This has gone to a completely different level,” she smiles. “And it’s been a while since I’ve been in something that is so universally watched as this is. Even when I did The Fall, it was popular, but it wasn’t Netflix popular, you know? So the level of recognition has gone up to what it was when I was younger.” The trouble is that she forgets. “I’m so used to sliding under the radar that there have been some situations recently where it’s just been… a lot. Travelling with kids and stuff. You don’t want to be that person. You want to be like, ah, thanks!”

‘The enthusiasm of fans, from being in science fiction, is intense’: in the X-Files, which aired from 1993 when she was 25. Photograph: Allstar/Cinetext/20 Century Fox

She has three children; two boys, Oscar and Felix, aged 10 and 12, while her daughter, Piper, is 24. At the height of X Files mania, when Piper was young, Anderson was followed constantly by paparazzi. “I couldn’t take my daughter to the park without long lenses and stuff. If that were the case here, I would not live here. I cannot stand it,” she says, crisply.

She was born in the US, but spent her early childhood in north London, before moving back to the States when she was 11. She speaks fondly of London, of its green spaces and its vibrancy, and it is where she has lived for most of her adult life. “In my formative years, my experience of private life was quite public. And I had a very different experience here in the UK, if one knows what neighbourhoods to stay out of and what restaurants to stay away from. And also, it’s just always felt like this is where I belong.” She is superstitious enough to curse herself for what she is about to say, but here, she explains, she doesn’t have photographers on her doorstep. “It’s that part of it that has made me really hate the business that I’m in, at times.”

When she is working, Anderson says, she can be quite unpredictable. “Depending on the day and what I’m working on, and my need to focus or whatever, I can be very relaxed and jovial, and then sometimes I can be serious and slightly shut down. I’m sure that must be confusing for people.” I tell her I wasn’t quite sure, from reading old interviews, who I was going to meet. She says that if she were to read an old interview with herself, which she doesn’t, she could tell you which ones happened during periods of intense paparazzi interest, based on how frosty she was. “It makes you paranoid. I just completely clam up.”

‘I had a very different experience here in the UK – it’s always felt like this is where I belong’: wearing her own Gillian Anderson for Winser London roll neck. Photograph: Gustavo Papaleo/The Observer

Today, she is perfectly open and friendly. Women, particularly, do seem to like her. “I do feel like a woman’s woman, and I go out of my way to be one. And actually I get so shocked and shaken when I come across women who aren’t. It really unsettles me.”

Anderson has played so many iconic characters, and almost all of them have shared a solitary, mournful quality, from Miss Havisham to Stella Gibson, from Lady Dedlock to Blanche DuBois in A Streetcar Named Desire, who is not always played as a model of restraint. Sex Education, though, has given her the chance to be funny. Her character Jean is a nightmarishly frank parent, for whom oversharing does not exist, and Anderson has run with it. Her Twitter bio is still Shag Specialist. “Oh, is it?” she says, coyly. “I guess I’m still the shag specialist. At least until Sex Education is off the air.” Her social media has certainly taken on a fruitier twist. “Mostly, that’s the penis and yoni of the day,” she says. People send in images of accidental genitalia, and her team backlogs them, and posts them. “It’s important!” she laughs. It also shows off her sillier side. “I mean, I feel like the silly side of me has always been there. Just in terms of the kind of humour. For a long time, Chewbacca was my boyfriend. I don’t know if you know that, but we were dating for a long time.”

She says this so matter-of-factly that it almost passes me by. Hold on, I say. Chewbacca? “I can’t remember whether it predates me taking a picture at a comic-con with the real Chewbacca. That might have been the beginning or it might have just been our first outing.” Either way, it turns out, she enjoyed a longstanding digital relationship with the Star Wars stalwart, which led to fans sending her a wild selection of Chewbacca memorabilia.

‘I guess I’m still the shag specialist’: as the no-boundaries therapist in Netflix’s Sex Education. Photograph: Sam Taylor/Netflix

“Then, when I knew that I had started to date somebody in real life, I had announced at some point that Chewbacca and I had broken up.” That was quite the declaration of commitment, to leave Chewbacca for your boyfriend. “Oh no, no, no. Let’s be clear. They didn’t overlap.”

Anderson’s boyfriend – no overlap – is Peter Morgan, the screenwriter and playwright who is currently at the helm of The Crown. Anderson is about to start work on the fourth season, in which she’ll play Margaret Thatcher; she is both keen to talk about it and wary of letting anything slip. “I haven’t quite figured out how to talk about her yet.” She has immersed herself in reading and watching everything she can find. “To a certain degree, it’s very helpful for an actor, at least in my experience, to slightly fall in love with the character you’re playing, regardless of what your opinion might be of them, if it’s a historical character, particularly. So I have.”

She is finding Thatcher “absolutely fascinating. Mostly because of her childhood. You could draw such a clear line from how she was raised and what she was exposed to in their religion, and how she was raised in the shop, and how she worked, and their work ethic and their beliefs. Just everything that came later stems so entirely from her childhood. But that in and of itself is fascinating, and – I’m not going to use the word forgivable, but one can find compassion.” She is excited to work with Olivia Colman, who will be her Queen, for the first time. “I’ve seen the third season, and she’s amazing.”

‘I like to think I am a women’s woman’: Gillian Anderson for Winser London silk georgette blouse; stretch wool trousers by Stella McCartney; shoes by Rupert Sanderson and earrings by Alighitheri. Photograph: Gustavo Papaleo/The Observer

In February, she appeared in London’s West End as Margo Channing, the role made famous by Bette Davis, in Ivo van Hove’s stage adaptation of All About Eve. It is the story of a famous woman facing the horrors of age in an industry that is not sympathetic to it, and I wonder if Anderson felt any significance in playing her when she herself was 50. “No,” she says, firmly. “In the film, Margo had just turned 40. The point wasn’t that I as an actress was trying to do something younger. In fact, we raised the ages of everyone by 10 years.” Her eyes flash, and she suddenly gives the impression of a cat teasing its prey. “Is there another part to that question?” she purrs.

Well, some of the reviews had an issue with the idea of you as an ageing actress at all; you weren’t “ageing” enough to be worried about ageing. “But that’s not really the point,” she says, with a sigh. “Firstly, so many of our issues about ageing, as men and women, have absolutely nothing to do with reality. It’s so much to do with our own perception or what we think other people’s perception is, to the point that 20-year-olds are having plastic surgery and Botox, because they believe that if there’s some sign of a wrinkle, or if they’re flat-chested or whatever, that that’s bad. So for a 50-year-old woman to be concerned about it makes sense, especially given that that’s her career.”

She is on a roll; she loves talking about her characters. “But also it wasn’t just about that. It was about her value, her value in her work, her value to her husband, not her value to her public, necessarily. So I was shocked at the small-mindedness of some of the reactions to it, in terms of just not understanding the psychology of human beings, and where lies fear, and one’s currency in one’s personal life and in one’s work life.” She takes a big breath, smiling. “Anyway!”

It will be a while before we see her on stage again. She likes to break up theatre roles, leaving gaps of a few years in between them. “I’ve had such fear and anxiety around it, and there have been so many times when I’ve been in the middle of it thinking, I must be mad to be doing it again.”

Blanche DuBois, in particular, was tough. “Streetcar was something else entirely. Even in the short runs that we did here and in the US, it really takes it out of one. I mean, there was a point where I thought I might be losing touch with reality, which is known to happen during that play.” Has she thought about doing a comedy? “Well, Sex Education is a gift in that way. There’s funny stuff in this second season.”

During Sex Education’s first run, Anderson’s hair was icy white. Today, it’s a light strawberry blonde again. She went white initially just to try it, for herself, and it seemed to fit Jean’s character, so she kept it. “But then my hair started to fall out.” She lifts up her hair to show me her roots. Her natural colour is a mousey brown, with only the odd grey strand, though she has thought about going grey. “Oh, I would, yes, and I’ve thought about it quite a lot, actually, when I had that hair. I absolutely would. It’s occurred to me that to decide to have it natural, as an actor, is quite a big decision. But it’s interesting, because when I first did it, I thought, it’s kind of cool, in an Annie Lennox, Billy Idol-ey kind of way.”

For a second, Anderson offers a glimpse of the teenage punk she was. “But when you’re in your 50s, it just looks like you’ve got grey hair. So I look forward to that, but I’m not ready yet, to deal with the consequences of it, which would be, presumably, that I would naturally be cast in a different zone of characters.”

‘I’m a bit of a hermit’: in A Streetcar Named Desire. Photograph: Tristram Kenton/The Guardian

We meet a few days before her 51st birthday. She celebrated the big day last summer with three small parties, in London, in Canada and in the US. “But it was only five people, six, and 13,” she says, merrily. “Those are all the friends I have.” She likes to be alone, and is a happily solitary person; the idea of a big party felt both presumptuous and like it was inviting “too much attention. It’s possible that were everyone in town, I would have chosen to do something with 30 people, but I don’t have hundreds of people in my life. I don’t have 300 people to invite. I mean, I probably do, but I wouldn’t imagine inviting people to fly over from LA.” She looks horrified at the prospect. “It felt better to gather in small groups.”

That suits her personality, anyway. “I think because I was an only child for so long, I don’t like to share,” she laughs. “I have spent a lot of my life being a bit of a loner and a bit of a hermit, and that’s my preferred state of being.”

She has chosen a funny career for someone who needs a lot of alone time. “Yeah, but when I’m not doing this, I don’t leave the house,” she beams. “It’s true! I really don’t. I work, or I’m with my kids. When I’m with my kids, I take them out. But I’m likely to sit in the corner.”

Styling by Hope Lawrie; lighting by Joe Stone; production by Emma Allan at Lemonade Productions; Waddington Studios; hair by Nick Irwin for anticollective.com; assisted by Ellie Bond; makeup by Florrie White at Bryant Artists using Surratt Beauty

Gillian Anderson’s new collection for Winser London launches today on winserlondon.com