‘People always talk about that scream,” says Indira Varma over salad and strawberries at the Old Vic theatre. The actor is recalling the howl she lets out in season four of Game of Thrones, after her lover Oberyn has his eyes gouged out by a hulking brute called the Mountain. Splatter flies and we cut to her character, Ellaria, who gives a blood-curdling screech.

What personal demons, I wonder, was Varma summoning to produce that? “It was the last thing they shot that day,” she recalls. “I had one go. We were losing the light. So it’s like…” She draws a breath and drags out an expletive until her voice squeaks. Then she says with a shrug: “You have to deliver.”

Varma, who has triumphed in Shakespeare, Shaw, Pinter and Hare, is now starring in Noël Coward’s Present Laughter at the London theatre. But she’s still best known as ruthless Ellaria, who we first meet embarking on a foursome with Oberyn and is usually to be seen writhing at his side, or scheming with her Sand Snake daughters.

In Matthew Warchus’s production of Coward’s 1939 comedy, Andrew Scott dons theatre’s most famous dressing gown to play the tousled matinee idol Garry Essendine. Varma is Liz, who never got round to divorcing Garry and manages his career with utmost pragmatism. This involves navigating his dalliances with debutantes and, in a fresh gender-switch, with predatory male actor Joe (Joanna in Coward’s original).

Coolheaded, elegant, shrewd: there’s a hint of Liz to Varma, who illustrates points with gestures placed as carefully as her words are chosen. “Liz is the one person who is direct with Garry, so he values that relationship. He is pulled in every direction by flattery and adulation. The thing about Liz that I love is she walked away from the marriage. She’s really powerful.”

This is Varma’s second Coward – she did The Vortex at the Donmar in 2002. I presume she saw his plays growing up in well-heeled Bath? Apparently not. “But I used to queue up for the Theatre Royal because they did £1 standing room tickets. I saw Lettice and Lovage with Maggie Smith. It blew my mind.” What else excited her? “People laugh but I love mime. I feel sad because I’ve kind of let it go.” Her career took her through different doors, she says. I picture Varma shutting out Marcel Marceau in a sad little mime. She might find a way back in, she insists – “a cat flap into that world”.

Varma, who is 45, was raised in an arty home by her Swiss mother (a graphic designer) and Indian father (an illustrator). Were they keen on her having an acting career? “My dad wasn’t. He’d just throw at me, ‘You should be a doctor.’ Utterly ludicrous. I was crap at science.” She went off to Rada. How was that? After a slight sigh, she talks instead about the fun of acting as a child: “There’s something so pure about being able to mess about, where there are no expectations.” She then remembers Rada as “great but quite intimidating”. There is a pause. “We all go through moments of self-doubt and going, ‘I’m the mistake.’ Or, ‘Maybe I’m not right for this. I don’t fit into what I think the theatre world is. I’m not useful to that world yet.’ To begin with, I felt like that.”

She graduated in 1995 and Mira Nair cast her as a servant turned courtesan in Kama Sutra: A Tale of Love, inspired by the ancient Hindu text. Nair was impressed by her “wilful gaze and imperiousness” and the film, shot in central India, was a “baptism of fire” says Varma. At 21, she hadn’t trained for film nor grown up on movies. Here she was debuting in a leading role requiring considerable nudity. “It was the first time I had to lose weight. I’d prided myself on being me – take me as I am! But the reality is that you’re there to serve the material. Suddenly you’re having to change yourself a little to fit this ideal.” She lost confidence and grew angry. But did she have a lot of trust in Nair as a director? “Yeah – and as a woman,” she says.

I ask if Kama Sutra narrowed the roles she was offered. “Oh God, yeah,” she says twice. “My name’s Indira Varma. It’s an Indian name. And I think, you know, if I had a Spanish name, people would maybe think I was Spanish. If I had a North African name, also. If I had an English name, I might be seen differently.” At drama school, one teacher suggested she change it but she thought: “I’m going to forge a path for those with foreign names!” Another encouraged her to keep it. “I’ve always been torn by that decision. I’m still in the business and I’m here at the Old Vic, but there have been moments where I’ve thought: bloody hell, I’ve missed out on that because actually they liked the tape and then someone went, ‘Bit too Asian – not really what we’re looking for.’”

At Rada, Varma had been cast as an old man – “and as a parrot!” But after Kama Sutra, she says, “all I was being offered was Indian exotica, women who take their clothes off”. She concentrated on theatre, playing Phoebe in As You Like It (opposite Stephen Mangan) and Bianca in Othello (directed by Sam Mendes). She had the distinction of not just doing Pinter but also starring with and being directed by the great playwright. She does an impressive Pinter impersonation, recreating his words of advice: “Nothing you do is wrong.” She laughs and explains he wasn’t talking “to me personally, daaarling! But if you are truthful, then nothing you do is wrong. That is the most liberating thing you can say to an actor.”

Back on screen, Varma was a hoot in matching Burberry cap and bikini in Bride and Prejudice, Gurinder Chadha’s Bollywood Austen makeover, looking on aloof in the Caroline Bingley role. On telly, in the satirical Broken News, she was newsreader Melanie Bellamy, frantically pacing around a studio. In Luther, she played humanitarian lawyer Zoe, whose grace contrasts with her explosive detective husband (Idris Elba). She was superb in Patrick Melrose, too, wracked with concern for Melrose’s mother Eleanor as they share a Ferris wheel.

This summer, she appears in Official Secrets, a film about GCHQ whistleblower Katharine Gun. She plays Shami Chakrabarti, the former director of Liberty who invited Varma to tea at the House of Lords. “I look nothing like her,” she says, “and she’s half my size.” Varma has just done a TV pilot, For Life, playing a gay prison warden. Curtis “50 Cent” Jackson is involved. “He’s done some music for it!” she laughs. “Really cool!”

Her industry, Varma says, requires actors to be Teflon on the outside but able to access their vulnerabilities in performance. “It’s a paradox.” She aspires to something similar when performing: “I’m in control of it but also not giving a fuck, so anything can happen. That tension is what it’s all about.” Does she carry characters around with her during rehearsals? “Prior to having a child, it was all-consuming.” Now Varma has a daughter with actor Colin Tierney, she switches off more easily – although they’ve been telling her to stop talking so loudly, reminding her she’s not on the Old Vic stage yet.

Several Thrones stars are doing theatre in London this summer: Gwendoline Christie is playing Titania, Julian Glover is doing Tennessee Williams, Faye Marsay is at the Donmar. Did she meet many of the TV juggernaut’s huge cast? “When I came in, in season four, our storyline had a wedding which meant everybody was there. It was really lovely.” What did her audition require? “I just had to, like, prowl around a little bit.” An actor friend had randomly emailed to ask why she wasn’t in the show. Varma thought: “Yeah, why am I not?” She emailed another friend who worked on it and got the audition.

Why is it so popular? She talks about clever storytelling, power struggles, then admits: “Oh, I don’t know. I haven’t watched the whole thing to be honest.” But she praises the Shakespearean richness in how characters contradict themselves. Varma’s real Shakespeares include a Titus Andronicus at the Globe that supposedly had audiences fainting. “Often they didn’t pass out in the gory bits,” she says. “The language is sort of more shocking.”

She remembers doing Twelfth Night and the power of Andrew Aguecheek’s “I was adored once too” line. “They call it a heart-stopping line. At both the matinee and the evening, a person had a heart attack in that scene. Somebody who’s a bit of a fool, who says stupid things, suddenly has one line that is profound. I did The Vertical Hour with David Hare. He said if you want to say something important, make a joke beforehand. I think Coward does that.”

Present Laughter’s title comes from Twelfth Night. Coward’s play was first called Sweet Sorrow but that was considered too gloomy for a wartime audience. “I think Matthew is trying to go for the Sweet Sorrow version,” says Varma before breaking out in a smile: “But there’s definitely laughter!”

• Present Laughter is at the Old Vic, London, until 10 August.