Legend has it that, in the early 20th century, Hungarian playwright Ferenc Molnár threw the keys to the New York cafe in Budapest into the Danube, in the hope of getting the cafe to open round the clock. Fast forward to 2018 and Florence Pugh, an actor and short-term resident at the cafe’s accompanying hotel, has made her presence felt in a similarly dramatic fashion. “You are making us feel unwelcome,” she complained recently to a snooty bar manager. “My friends and I have chosen to come here and we want to have a good time.” Her companions – a clutch of fellow up-and-coming actors who were also filming in the city, including Call Me By Your Name star Timothée Chalamet – trailed behind her.

The 22-year-old tells me this story as we sit in the opulent Renaissance-style bar upstairs. But it seems like all is forgiven: Pugh’s vodka, soda and fresh lime arrives moments after she orders it. I suggest they may be a bit scared of her and she lets out a hearty cackle.

Whether or not you know her name yet, Florence Pugh is as formidable in person as she is on screen. You might have caught her lethal performance in William Oldroyd’s chilling 2016 film Lady Macbeth (for which she was awarded a British Independent Film Award and nominated for a Bafta), or seen her play Cordelia to Anthony Hopkins’ King Lear earlier this year. Later this month, she’ll take the gutsy lead in BBC One’s big John le Carré adaptation, The Little Drummer Girl.

With Alexander Skarsgård in The Little Drummer Girl. Photograph: Jonathan Olley/AP

Filming the six-part espionage thriller under the direction of Park Chan-wook (who made 2003’s hyper-violent neo-noir Oldboy) was so exhausting that Pugh planned to have the summer off; she even considered taking up knitting to relax. “It was such a rewarding but intense shoot,” she says. “I was scared, of course, but I always like to be. There has to be some level of fear.”

But then Ari Aster, horror film director du jour, came calling, asking her to take the lead in Midsommar, the follow-up to his critically acclaimed debut Hereditary. Pugh had just come off a night shoot when she FaceTimed him, and “usually when you do those Skype [meetings], you beat around the bush, but we were both so tired, we were like, ‘I’m yours’,” she says softly. “We both got told off by our reps for doing that, but it was one of those amazing moments.”

It’s Midsommar that has brought the Oxford-born actor to Budapest. In a few months, she flies to Boston, because Lady Bird director Greta Gerwig has cast her in a big-screen adaptation of Little Women alongside Saoirse Ronan and Chalamet. This time last year, she was filming King Lear, before moving on to Scotland to make the forthcoming Netflix film Outlaw King. Whirlwind doesn’t cut it. “I don’t have a home,” she shrugs. “With the life I’ve been lucky enough to live in the last two years, I’ve had to live out of bags.”

Comparisons between The Little Drummer Girl and its multi-award-winning 2016 predecessor The Night Manager will be unavoidable, from the exotic filming locations (this year’s drama is a glowing advertisement for Greece, rather than Mallorca) to the all-star cast (Alexander Skarsgård plays Israeli intelligence officer Becker, with whom Pugh’s character, Charlie, becomes entangled). Will there be an equivalent to the #Hiddlesbum phenomenon, when Tom Hiddleston’s naked bottom stole the scene from Elizabeth Debicki? “I think there’s a Pugh bum at some point. But that doesn’t sound as good! After Lady Macbeth [in which she appears nude], it was… I mean, everybody knows everything now.”

We meet soon after Outlaw King has just premiered at Toronto film festival, to mixed reviews. Chris Pine stars as Scottish king Robert the Bruce, with Pugh as his queen, and most of all, the critics seem preoccupied with Pine’s “full-frontal nudity”. “It was all on Chris Pine’s penis! It’s just a penis,” she laughs.

With Chris Pine in Outlaw King. Photograph: Netflix

That shoot coincided with the start of the #MeToo movement, which Pugh says was a heightened experience because she was one of the few women on set. “It was during the time everyone was like, ‘We need more women.’ But I was on set with 100 of these incredibly intelligent, wonderful men and we all looked after each other. It was an amazing moment because, while the industry was kicking off, it was like, ‘OK, yeah, here is an example where there aren’t that many women in this film and that is sad. But I get to be here, representing this woman whose storyline has been stripped from her.’”

Equally empowering, she says, was watching early footage at the wrap party – something that’s normally awkward, because “it’s so difficult to not look at your flaws”. But not this time. “Everybody was gross and dirty and hairy; I was over the moon to be watching something where not one person was movie-ready. As beautiful as cinema is, it’s a massive part of the problem of why we look at ourselves in the way we do. What we don’t realise when we watch a normal film is how many times someone has run in just before a shot quickly to wipe away that sweaty moustache. You never see a normal spot, a bag under the eye or an unplucked eyebrow, because that’s not how Hollywood works.”

Pugh had a gentle introduction to the industry, aged 17 (and still in sixth form), with a part in the enigmatic coming-of-age drama The Falling (2014), largely because director Carol Morley prevented the cast (most of whom were school age) from watching themselves on screen. “We weren’t allowed to look at the monitor because we would be acting for vanity,” Pugh says. “And from then on, I’ve tried to keep that as part of how I work.” It is this unpretentious attitude that Morley has said reminded her of a young Kate Winslet, and which convinced Oldroyd that Pugh could carry his 90-minute Lady Macbeth.

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The bar’s resident pianist takes his seat at the grand piano for the evening, next to our table. “Oh, hello!” Pugh giggles as he begins a lively rendition of The Sound Of Music. “Whoa, this is amazing!” And it is, until it reaches a cheesy crescendo. We retire politely to a quieter corner.

I don’t want to change myself. But if you go to Hollywood as a canvas, they'll make you into what they need you to be

On paper, Pugh’s transition from impressive newcomer to commanding lead in the space of two years appears seamless, but then there isn’t anywhere on her IMDB profile to list the short-lived Hollywood encounter that she says almost put her off her career entirely. “It was the first time I’d gone to America,” she recalls of the audition that led to a TV pilot, Studio City, co-starring Heather Graham and Eric McCormack, tipped to be a series that would run and run. “It was mega news. I was going to be doing a TV series with Hollywood stars, probably for a good half of my life. It was where I wanted to be at some point in my career and I was there on my second job.”

When did she realise it wasn’t all it was cracked up to be? “There was a kind of, ‘OK, so, you’ve got the part, but this is what we need from you, and this will happen straight away.’” What did they ask her to do? “Just to be in… to be ready for their series, to change me.” In other words, she means, to lose weight. “What I’ve noticed about Hollywood is, if you go out there shouting about who you are, they will love you for it. But if you go out not knowing what it is that you’re representing, and you are just a canvas, they will make you into the thing they need you to be.”

As Lady Macbeth. Photograph: Allstar/Sixty Six Pictures

The pilot didn’t take off and, two months later, Pugh auditioned for Lady Macbeth. “I swore I would never go back [to LA] until I knew what it was I was representing. After Lady Macbeth, I was applauded for having normal bum cheeks, so I was like, ‘OK, this is my shout. I’m obviously this,’” she says, gesturing to her petite, toned, 5ft 4in figure, “and this is all I’m going to be. I don’t want to feel like I have to change myself or my image. I was lucky to have the upbringing I did and the knowledge that this [pressure to look a certain way] is nonsense.” She will never have a willowy, 5ft 10in, model-actor frame, and hadn’t expected to be judged for it. “I knew this happened, but I didn’t know it was going to happen like that, to me.”

Pugh grew up in a close, creative and affluent family. Her mother is a dancer and dance teacher, while her father owns a chain of restaurants in Oxford. She is the second youngest of four siblings, all of whom pursued drama. “We’re like the Von Trapps, but not quite as pretty or perfect,” she jokes. Her older brother Toby Sebastian is best known as Trystane Martell in Game Of Thrones, while her older sister Arabella Gibbins is a stage actor. “She is the only one who actually studied, so she’s the one with all the knowledge,” Pugh says. I wonder what the elder two make of their little sister rising so rapidly through the ranks; but she denies any competition and obviously idolises her brother, who is four years older and started acting at 16. “I remember watching him for years so, by the time I stepped up, I kind of knew the harsh reality of how things worked.”

Despite a privileged education at two private schools in Oxford (Wychwood, then St Edward’s, whose alumni include Laurence Olivier and Emilia Clarke), Pugh is adamant it didn’t do her any favours. “For a long time it was like, ‘I know these people [the school] don’t back me’, because they didn’t. When I wanted to do The Falling, I was told it wasn’t going to work, which was shocking to me, because [drama is] the only thing I’ve ever been good at. I don’t think there’s enough listening or thinking time. Having to make life decisions when you’re 14? My dad would be like, ‘It’s all a load of toss!’”

Pugh was in and out of hospital as a child with collapsed airways and asthma, and the family moved to Spain for three years in the hope that the warmer climate would help. “Even though we moved out there for other reasons, looking back on it, I’m so happy I had that childhood – in and out of the sea naked, cycling down the road in my knickers, and bartering with the sweet shop owner,” she reminisces. In other words, seeking an audience, even then.

With Anthony Hopkins in King Lear. Photograph: Ed Miller/BBC

Her first memory of performing was playing “a northern Mary” (her idea) in a school nativity, when she was six. “I remember hobbling on to the stage, going [she adopts a broad Yorkshire accent], ‘Ooh, me varicose veins!’ and everyone pissing themselves.” Jokes aside, “It was the first time I knew the power of being on stage. I remember thinking, ‘Oh God, they’re waiting for me, they’re listening to everything I say and I have complete control.’ I still feel that now. How everyone is hanging on to your every word; how they are going to feel how you want them to feel.”

Pugh considers Emma Thompson “a massive mentor” – they met on the set of King Lear last year, just as the revelations about Harvey Weinstein were causing shockwaves. “The industry was so sad and so desperate for leadership that to come into work and be around Emma, and Emily Watson, and that loud female wisdom all day was so powerful. There wasn’t a day she didn’t educate me on something, or give me a book or podcast to listen to.”

Before Pugh leaves for dinner with her Midsommar co-star Jack Reynor, I ask who else she dreams of working with. And then I remember she’ll meet Meryl Streep when she starts filming Little Women (Streep will play Aunt March). “I can’t wait to meet her, but I’m so scared,” she confesses.

At least you’ll have your friend Chalamet there, I say. “I accidentally called him Timothée Chalamala-bing-bong to his face,” she laughs. “He was like, ‘What?’ And I was like, ‘Nothing!’” High-spirited and playing by her own rules: if this is the face of Gen Z’s Brat Pack, Hollywood is set to have a lot of fun.

• The Little Drummer Girl starts on BBC One later this month. Outlaw King is on Netflix from 9 November.

Makeup: Naoko Scintu at The Wall Group using Omorovicza. Hair: Wilson Fok at Eighteen Management using Bed Head by TIGI. Photographer’s assistant: Hugo Volrath. Fashion assistant: Penny Chan.

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