You look great, I tell Fiona Shaw. Must be the pig's placenta. Shaw (60), pretty and angular in a soft grey shirt, smiles enigmatically from the sofa of her north London home. Pig's placenta is her MI6 officer Carolyn Martens's beauty secret in the second series of Killing Eve, Phoebe Waller-Bridge's dark, wildly successful thriller about a psychopathic female assassin called Villanelle and Eve Polastri, the agent hunting her down.
But pig's placenta aside, Shaw puts her youthful appearance down to "not being in the theatre every single night". Which is where she's been for pretty much the past 30 years. Formerly known for a huge body of iconic stage roles, including Hedda Gabler, Medea, Electra and Richard II, as well as for playing Aunt Petunia in the Harry Potter films, Shaw's fame is now more attributable to her transition to television.
In Killing Eve, Waller-Bridge has taken a genre that's a little worn out - the international-assassin thriller - and given it a completely different slant. The show won five awards at the Baftas last month - including Outstanding Drama Series and Best Supporting Actress for Shaw, who in her acceptance speech referred to the "glass-shattering genius" of Waller-Bridge.
Carolyn Martens, head of Russia at MI6, is a perfect example of Waller-Bridge's wayward approach. Carolyn is very still. Arch, deadpan, erudite, severe. But she has a tipsy flirtatious side, and a hidden messy streak. She's oblique - and the viewer doesn't know how much she knows, or whether or not to trust her. Nor does Eve (played superbly by Sandra Oh). "I once saw a rat drink from a can of Coke there," Carolyn says earnestly to a bemused Eve when they're in a rubbish-strewn alley. "Both hands. Extraordinary..."
'Carolyn's a joy to write,' says Emerald Fennell - best known as an actor for Call the Midwife, and The Crown's new Camilla - who took over from Waller-Bridge as lead writer on the second series (Waller-Bridge remains an executive producer) "The character is entirely dependent on Shaw. She is unbelievably brilliant, funny, and scarily clever. In one of the episodes, another character mentions [11th-Century saint] Anselm's ontological argument [for the existence of God], and during the read-through it transpired that Fiona had written a literal thesis on it. Quite embarrassing for those of us who only had the most passing Wikipedia acquaintance with Anselm (me). Fiona's cleverness and wit are built into the fabric of who Carolyn is.'
Shaw compares playing the part to keeping a secret at the same time as delivering a line. "It's not easy to do. I have to say I do lose sleep over it - I'm playing somebody very different to what I normally play. Normally I have to expose the truth.
"When I'm in the theatre, where I would be swimming with the tide, it's my job to lasso the audience and to make sure they understand the moral dilemma of the piece - that's what leading players do. You are sort of the MC for the night...
"In Killing Eve, most of my work is about knowing more than everybody else in the scene and hiding it. And it's a terribly lonely thing to do. It feels all wrong - like rubbing my tummy and patting my head at the same time. I want to smile, I want to make jokes - but you are left with an ambiguity. You don't know whether I know I've made a joke or not. It's very good exercise for me."
Earlier this year, Shaw appeared in the second series of Waller-Bridge's other seminal television show, Fleabag. Initially, she had to turn it down because she was directing Cendrillon at Glyndebourne (directing opera is another of her talents). Then Fleabag overran, and she was able to join in after all.
Waller-Bridge is the definitive young auteur of our times, and it seems she can do no wrong. The stage production of Fleabag - coming to the West End in August - sold out in an hour. "I feel she's nearest to Oscar Wilde," says Shaw now, "which is to say she's greater than the sum of her parts." Comedy, in some ways, is quite a conservative thing, Shaw thinks, although it may not seem that way. "But it always has a frame; it stays within that frame but it kicks against it, like a child in a playpen.
"Phoebe develops people so they turn into bigger people, and bigger people, and I think that's a confidence that's come with her previous work. She's mastered one form, and she's been able to take the gate off and let the characters run out into the field - and yet they're still intact, and the audience follows them. It's superb."
For actors, she says, that approach couldn't be better, which is why so many of them, including herself, Andrew Scott and Kristin Scott Thomas, are desperate to work with Waller-Bridge.
"I could have played the boss of MI6 and pretty well come up with the same 'ker-chings' every week," says Shaw, who also played an MI6 officer in BBC One's recent Mrs Wilson, "but that isn't what happens in Killing Eve."
Waller-Bridge was always on set during the making of the first series, constructing and reconstructing her work like a Rubik's Cube. When Sandra Oh pointed out that the actor Sean Delaney, who plays Kenny Stowton (a young ex-hacker recruited by MI6), looked like Shaw, Waller-Bridge decided to make his character her son in the story, and wrote it in, just like that.
Shaw is taken aback by the popularity of Killing Eve, and particularly by the wide demographic to which it appeals. "Fathers and sons watch it, mothers and daughters, husbands and wives. I don't think it bears much analysis. I suppose it has no politics, it's fantasy really and that's why I think the violence is nearly allowable - it's cartoonish."
It's also stylish - the music is great; the costumes are superb; the graphics are slick - and clearly a high-budget project, shot in London, Berlin, Paris, Amsterdam. Shaw is often recognised for playing Carolyn. She was amazed when, on a New York street recently, someone reacted so wildly on seeing her that she appeared to be having a fit.
Fiona Shaw grew up in Montenotte, Cork, with three brothers. Her father was an ophthalmic surgeon and her mother was a physicist. She always wanted to be a tennis player, she says, but instead studied philosophy at University College Cork and then went to Rada in London.
She still remembers the audition: the teacher told her later that she smelled of libraries. That's because it was as if she was born into the 19th Century, she says now, compared to the other applicants.
She was not cool. Everyone was instructed to wear a black dress. Shaw had made her own - and it was a bit wonky. She was terrified.
"I remember some American guys at the audition were doing press-ups, and people were talking about the Royal Shakespeare Company - and I thought, I haven't a hope in hell."
Hearing she'd got in was, she says, "one of the nicest moments in my life". She is still an advisor at Rada. She worked hard and went straight into the cast of Richard Brinsley Sheridan's play The Rivals at the National Theatre, alongside Michael Hordern and Tim Curry ("I couldn't have been in better company").
Her father had his reservations, "but I think he thought I would come to my senses". A year later she joined the RSC. Her parents came to watch her, and her obvious success calmed her father's fears. "He got much more interested when he could read about me in the paper - in the end he was incredibly supportive - but I had to go through the firewall of his disapproval for a while."
Then her brother Peter was killed in a car crash. Shaw was 28 at the time. "That was such a blow to my family. Neither of my parents could really function for about a year after that. It was very hard for them."
Two years after her brother died, she was offered the role of Electra (for which she won the first of two Olivier Awards), and in some strange way found herself channelling her grief. "I loved comedy - but then I was asked to do Electra. Deborah Warner was directing and I thought, oh well, I'll give it a go. But I didn't see the point of a tragedy and I couldn't do it at all. And slowly I realised that it's much more about yourself. And I discovered a new world through tragedy.
"Electra has a brother who she thinks is dead - and I knew something about having a brother who was dead. I wouldn't say in any way that I was mainlining my brother, but I suddenly realised that plays are about life, and domestic tragedies are heightened in the theatre - but they are the same as all our tragedies - and that is what the theatre is for. I don't know why I hadn't worked that out before." It was the first of many collaborations with Warner (with whom Shaw also had a relationship), which went on to include Hedda Gabler, a controversial Richard II at the National in 1995, and Brecht's Mother Courage and Her Children.
Shaw's first major film role was in My Left Foot with Daniel Day-Lewis (1989). Soon after came Three Men and a Little Lady (1990), and later the Harry Potter series. It is the former, she says, for which she is most recognised by the public. She has just finished filming Ammonite, an historical drama directed by Francis Lee, in which she plays Elizabeth Philpot, a palaeontologist, opposite Saoirse Ronan, and Kate Winslet as fossil hunter Mary Anning.
Was there a moment when she felt she had made it on her own terms? "I think I was very lucky. I didn't do film on my own terms - you're either a film star or you are not - because I was so obsessed with the theatre when I was young. Probably I would have had to go and sit in Hollywood - but I wouldn't do that.
"But I have done a lot of things on my terms, just being allowed to do those shows: Electra, Hedda Gabler - and Richard II, which seemed quite nerve-racking at the time, but that was part of the thrill of it. So I've always tried to do things which are hard to do - maybe even to a fault.' She has never, she says, been trapped in a long run of a West End show she didn't want to do. "There always had to be an element of experiment." And she loves taking theatrical risks. Like her rendition of The Rime of the Ancient Mariner, which premiered at Epidaurus in Greece in 2012, then went to the Old Vic Tunnels in London in 2013, and on to the Brooklyn Academy of Music. Or (with Warner) the dramatisation of TS Eliot's The Waste Land she performed in locations including an old disco in Brussels and a former munitions factory in Dublin. Last month, she revisited it in New York, reciting it against the backdrop of a sculpture exhibition in Madison Square Park - it wasn't advertised but word spread and people came in their hundreds. "It was a huge pleasure, it happened almost by accident."
Shaw's father, Denis, died in 2011, but her mother, Mary, is 93 and still lives in the house that Shaw grew up in. She drives, plays tennis. When Shaw goes back home she sleeps in her old bedroom. "Well, I try not to - it's awful to sleep in the bedroom you had when you were 14. Some things are still exactly the same, the wardrobe and the poster of Narcissus - do you remember those terrible posters?"
Shaw lives between the house in north London and New York, where her wife Sonali Deraniyagala, a Sri Lankan economist, teaches at Columbia University. In 2004, Deraniyagala was on holiday in Sri Lanka with her family when they were caught in the tsunami. Her husband, parents and two young sons died. For years, Deraniyagala lived in a haze of madness and grief. In 2013, she wrote an extraordinary memoir, Wave, which won several awards and had some remarkable reviews. Shaw was in New York performing in Colm Toibin's The Testament of Mary when somebody gave her Deraniyagala's book. She read it in her dressing room. "I thought it was the best thing I'd read for a long time, on any level." She mentioned this in an interview. Then things came together in a felicitous way: Shaw was supposed to return home straight after the play closed, but she had a serious ear infection (due to having to disappear for several minutes in a plunge pool every night on stage), and was unable to fly. She stayed in New York and went to a Laurie Anderson concert, where she was invited to Anderson's book club - they were reading Wave - to meet the writer.
"I was so surprised that she was that person - not the person in the book. We spent half an hour chatting. When I left I thought, I have just met life." She pauses. "The play had been exhausting and so much about death, and I was feeling so miserable, and I thought, that person is life - even though she has had more death than you would wish on your worst enemy, there's a force in her that is just life."
When Deraniyagala came to London they met up again. "Very quickly I thought, I just want to live with this person, and it's been one of the most marvellous things to happen - but it was also highly unlikely. But in my profound self, at my core, I thought, I want to live with this person. It was deeper than anything. And thankfully, she thought the same - it's been a beautiful thing to happen at this stage of my life."
They got married in Islington town hall in January of last year, and then had their wedding party on the day of the royal wedding. "It was fantastic. Half of Sri Lanka came and it was a very beautiful wedding - everyone was wearing saris and looking gorgeous. My mother played the piano and sang, which was quite hilarious, and we had a band and dancing, a very late party."
Her mother sounds very enlightened, being 93. Were there no raised eyebrows at the fact that Shaw was marrying a woman? (As well as Warner, she previously had a relationship with the actor Saffron Burrows.)
"More than raised. But it's fine - the world is changing fast. My mother was very good about it and also very impressed by who Sonali is."
So she's not religious? "Oh she is, but she's also terribly funny about it. And she's a sort of nouveau old person. I think being old is quite a shock for her - and a lot of friends are dead, and some of them have lost their minds. But she's very well - and very happy for me."
Deraniyagala and Shaw have been to Sri Lanka several times to visit Deraniyagala's aunt, and love it there. Given what happened to Deraniyagala, recent events - the bombings at Easter - must have been completely destabilising. "Sri Lanka has been very much at peace for the last 10 years since the war, but the scale of what happened with those 250 people dead - it's as big as 9/11 for them, because it's such a small island. They were innocent people, and it's the most depressing thing - and terribly hard for Sonali - because the mass funerals are very near to the mass funerals of her family; it's terribly hard for her to revisit that time. It feels a bit like a natural disaster because it has no rhyme or reason." Shaw is about to start work on a film called Corvidae, a thriller co-written and directed by young filmmaker Joe Marcantonio. Then Killing Eve, series three, is on the cards for next year. If she had to choose only one discipline to work in for the rest of her life - theatre, film, opera or television - which would she choose?
"That's a cruel question. I would find it very difficult, but I would probably say television because I've done 30 years of the theatre. I've worked morning, noon and night, sometimes rehearsing all day and performing every night for decades. That's a lot. I don't have any great need to do that again.
"And I'm very interested in television now because one of the new pleasures it's given me is the scope of the audience. We used to be thrilled when we had 500 people, or 1,000. Now we have millions and you think, oh God, this is so obvious. Especially when the material is of such great quality and so uncynical. A few years ago they were just churning television out, but they aren't now - it has some of the best minds working in it. So I feel in a way like I'm in the same profession, it's just the shape of the stage which has changed."
In the end, she says, in any medium, it all comes down to the same things she has always aspired to, and which she is so excited about - that sense of infinite possibility in a role, and the thrill of making the heartbeat of the audience quicken.
Fiona Shaw will be appearing at the Borris House Festival of Writing & Ideas today. www.festivalofwritingandideas.com 'Killing Eve' is shown on BBC1 on Saturdays at 9.15pm