When I went to see Vanessa Kirby starring in Julie at the National Theatre, it turns out I picked “a really bad night. Oh God everything went wrong,” she says when we meet a few days later, in a café in Chelsea where she has just ordered scrambled eggs. In one climactic moment she has to kill a budgie on stage, but the blood capsule didn’t burst until well after she whizzed the fake bird up in the food processor. “That happened two nights in a row! But it was better than before, when we used to start the scene with a real budgie and then kill a fake one, because one night the real one started tweeting after the lights went down, when he was supposed to be dead. I was trying to shut him up. He was called Gordon. We had to get rid of Gordon. There have been letters to the theatre: ‘We need to know that Gordon has not been harmed.’”

Kirby is a 30-year-old actor from London, a galloping laugh a minute, and quite probably the future of British acting. You may know her as Princess Margaret from Netflix’s The Crown, a role she describes happily as “the gift that I was given”, and which turned what could have been a staid drama about duty and class into something much more delicious. She gave Margaret a youthful vulnerability – we saw the damns she had to give before she stopped giving any – and now, after two series and winning a Bafta, she is handing the role over to Helena Bonham Carter, who will play the older incarnation. And Kirby is gutted.

“The Crown was the best time of my life,” she says, in her quick voice. “Saying goodbye to it was awful, I really grieved it, actually.” Kirby kept a photo of Margaret on her bedroom wall and used to gaze at it, wondering What Would Margaret Do? “The easy route would have been for me to just play her as the version of her who comes later, the public persona of her that is so – I don’t know the right word – gauche?”

They could have sent you to Mustique!

“I know! Livid! But I wanted to try and find the person she was before she hardened, before she became bitter and self-loathing, which is what I sensed. I wanted to find the torment that’s underneath those things. That, for me, made a real woman, even though the circumstances were ridiculous.”

She played opposite Claire Foy as the Queen. Both of them have just been nominated for this year’s Emmy awards for The Crown. I ask what it’s like to be on the receiving end of the enigmatic, brooding looks that Foy’s Elizabeth so regularly deploys.

“Oh, she used to give me the look in our scenes together and I’d just be feeling, aaaargh – you’re so internal! You’re so good! You’re so subtle and I have to try so hard to rein it in! But Claire was much better about the show ending than I was. She said it was because I had such a personal synergy with Margaret, whereas the Queen remained a mystery to her.”

It transpires the real Queen is a fan, though. Kirby only knows this because a friend of hers was at a fancy party recently, “where he didn’t know a soul so when he heard some people discussing The Crown he was like: ‘Actually I know someone in that.’ They were like: ‘Cool.’ He goes: ‘No, but I really know someone in it,’ and, meanwhile, this girl says: ‘Well my granny likes it,’ and he suddenly realises her granny is the Queen. It was Princess Beatrice. Although, I told someone else recently it was Eugenie,” she laughs, “but I got that wrong.”

Kirby grew up in Wimbledon, south London, the middle child of three, and attended the private Lady Eleanor Holles School. Her mother, Jane, had been the editor of Country Living and her father, Roger, one of the country’s leading prostate surgeons, “always watched loads of films with me – totally inappropriate ones like Midnight Express when I was about six. He put all films on. I think my sister was five when he took us to the cinema to see A Perfect Murder.” They were also taken to a lot of plays, “and I got really bored until I was about 11 and then suddenly it clicked for me, like: oh, when theatre’s really good it can be transformative. More than anything, it made me understand people.”

At primary school, “It was always the drama side of things where I felt the most alive,” she says. “The most myself. I was quite badly bullied for a few years and I became self-conscious about everything I did in relation to the bullies. But drama was the place where I didn’t.”

Was it other girls?

“Yeah it was… systematic. Quite awful. A teacher said to my mum on my very last day of school: ‘She survived it. She’s done it,’ which means they knew it was happening.”

Strangely, Kirby doesn’t sound remotely bitter about it and mutters a half-finished thought about it perhaps being a useful experience now. She describes her childhood as very happy and she knows how socially and financially privileged she was, but she also suffered from giardia, an intestinal parasite, which went undiagnosed for a long time and made her feel permanently nauseous, as if she was about to vomit. “All these nightmare injections, pills up the bum, all of it. Prodded around from age nine to 11.”

At school there was a noticeboard with a picture of Ben Whishaw as Hamlet at the Old Vic on it. Kirby stole it for her bedroom wall, went to see the play three times and became obsessed with him, which was not helped by bumping into him on a London bus. She was in amateur local productions at the time, but after studying for an English degree at Exeter and then giving up a place at Lamda to go straight into work as an actor some years later, her first big chance was on The Hour – starring… Ben Whishaw.

The director was tough on her, which may have been because: “I wasn’t paying any attention to the scene. In my head it was just alarm bells going: ‘Oh my God that’s Ben Whishaw.’” Afterwards she had to tell him everything. “And it felt good to finally confess my infatuation. Of course, he was with his boyfriend.”

Hollywood came calling and she’s had to become better at dealing with famous men since being cast in the sixth instalment of the Mission: Impossible films, out this month and starring Tom Cruise. I ask what he was like. “Such a pro. Absolutely disciplined; super enthusiastic. Always wants everything executed at a super-high level, so you have to train really hard.”

With him?

“Oh God no, without him.” She laughs, groaning. “I think that would be… I did say to him at one point: ‘I am never getting on a running machine with you.’ But I learned a lot about work ethic from him. I never thought that stunts and action would be my genre, but I’m understanding now that you can transcend genre, as long as you try and find the real woman behind the part.”

It struck me, watching Julie – which is Polly Stenham’s rewrite of the Strindberg play Miss Julie, and set at 3am at a druggy party in a wealthy house in Hampstead – that Kirby could have played the heroine in a much sexier fashion. Instead, she chooses to drag her body around with her as if it brings her discomfort. The reviews have been kind to her, but not to the script or production, which tend to say it all lacks chemistry. Kirby diplomatically says the problem is: “It’s such a huge space, it’s not an intimate theatre and sometimes the space dictates the parameters.” I’m not convinced she’s enjoying it all that much.

Still, the current feminist awakening of Hollywood has had a real impact on Kirby, who has risen to fame at the perfect moment to seize it. She is working on her own ideas, too. The week after we meet she will fly off to work on an unnamed film project she’s developed with Adam Leon. “He’s the best New York film director, I think.” It’s inspired by an article about a woman who entered a fugue state and went missing in the big city. They have cast a group of renegade, gender-fluid young Brooklynites to play her new friends, and Kirby scrolls through her phone to show me photos of these genderless kids she finds so mesmerisingly beautiful. She is also developing a film of her own with Ben Caron, who directed her in episodes of The Crown, and making “something about babies who are born addicted to drugs and how society treats those mothers”.

Partly this seems like an attempt to get away from the wealthy-woman-in-gilded-prison roles. “I feel like now, more than ever, it’s all of our responsibility to have other things represented on screen. There have been so many male stories on screen, or stories of women written by men, so she’s the wife of someone, the girlfriend of someone… It’s only now I realise that looking back, all the scripts I’ve read over time, unless they’re really small indie films, the women have always been fantasy figures, always viewed through the male lens, almost cartoony.”

Her boyfriend, Callum Turner, is also an actor, and recently they were on a plane together, both with a pile of about 10 scripts to read through. “In every single one he was the central protagonist and the women were helping the leads. Out of mine, about two of my parts were the leads – and then you knew that someone like Jennifer Lawrence would be doing it. So we women have got to be the generators of the material and, in order to do that, we have to understand the system we’re in, which I’m really trying to do.”

Kirby has a friend called Sarah, “who says it just pisses her off, all these Hollywood actresses getting on the red carpet and sounding off about #MeToo, etc. She says, what are they actually doing? I say I know, but these are the women who will be on the front pages of newspapers, for better or worse, and then it leads to real change in other industries, too. Media is the controller of everything.”

Another close friend is the writer Dolly Alderton. They even share the same therapist, which made Kirby very amused to read all about said therapist in Alderton’s recent bestselling memoir, Everything I Know About Love. Yet another friend is Anna, with whom Kirby and her sister share a flat in Tooting. “So we’re like three sisters. No idea why we live in Tooting, though. I think it was cheapest.” Their home has calmed down a lot since Kirby became so busy. “It used to be mad parties non-stop and the vibrations going through to the little old lady who lives next door – her house was constantly shaking at 4am.” I can’t imagine Kirby upsetting old ladies – she seems too sweet. Did the woman complain? “Sometimes, yes,” Kirby admits, with a shamefaced twinkle in her eye.

Still, she seems entirely unafraid to call the shots on the big guys now. “My only little area of change is to be in a big movie and say no, I’m not wearing a short skirt, I’m not showing any skin, I don’t want slapped-on make-up,” she says.

And if the action film wanted to give you robo-tits? “I would say absolutely not. I don’t care any more. I feel more able to say that now. I’m in a slightly luckier position, but also the times now support it. I don’t want an arse shot – well, not that they’d want one of my arse. But I don’t want to be shot through a lens of sexualisation. That’s not me. That’s the distorted feminine and the distorted masculine that is creating so much of the toxic energy in our society.”

It is unusual to hear an actor ask quite so many questions in an interview. As she says, she is fortunate to have risen to fame in a time that allows it, with other women having begun to push the boundaries. But Kirby is questioning everything. Still, you can only fight off so much of the culture. We say goodbye and she picks up her bag of M&S shopping and heads home to watch Love Island, during which, she says happily, she will “feel my brain turning into disgusting nothing”.

Mission: Impossible Fallout is in cinemas from 25 July. Julie runs at the National Theatre until 8 September. Make-up by Kay Montano at The Wall Group using Apothesis, Le May de Chanel and Chanel Le Lift. Hair by Johnnie Biles at Frank Agency using Moroccanoil One. Fashion assistant Penny Chan