Costner’s confidence in Miller was well-placed; she is wonderful as Frances, bold and fragile, someone who has lost nearly everything but insists upon survival. I ask what it was about the character that resonated with her. “If there’s one thing I’ve gained from the life I’ve led it’s a sense of resilience, fortitude – which sounds like I’m complimenting myself, but that’s not how I mean it. It’s like being forged in fire. I would have loved to have not been forced into that resilience, but I have, and that’s a part of myself that I brought to Frances.” At its Cannes premiere, the film received a seven-minute standing ovation.

Dress, Celine Plein Soleil

Miller always knew she wanted to be an actress. She was born in New York, her father an American banker, her mother an English former model. The family relocated to London when she was 18 months and her sister Savannah was aged four. Within a couple of years of the move, her parents divorced. “I had quite a complicated family situation, and I was the clown, the all-singing, all-dancing, joke-telling prankster,” she says. “I was always putting on plays and dressing up. I think, back then, it was to do with entertaining people.” It’s a classic manoeuvre for an empathetic child who senses tension, trying to lighten the mood. And in many ways, this remains Miller’s modus operandi. She is charming, funny and friendly, welcoming me into her home with biscuits and tea, even though she has a new baby and is jet-lagged, having landed from New York the night before. The trip involved attending the Met Gala as part of the Chloé ensemble, which included Greta Gerwig and Emma Mackey, but was less glamorous than it sounded, or indeed looked. “We flew to New York on Sunday with our nanny and, on landing, she got deported. So it was a random scramble of trying to find a babysitter, and stressful because I’m breastfeeding. It was a bit of a trip.”

Cardigan and shorts, Gucci

New York, though, is familiar territory. It was where Miller learnt how to act. She had been sent to board at Heathfield School in Berkshire aged eight, which she says she loved, “but I felt like it was just very small and insular”. She finished school a year early, and three days after her 18th birthday, arrived in New York. “I was craving adventure. I’d watched the movie Fame. I was seduced by the idea of New York, people wanting to achieve something that felt unachievable. I had the sense that here was somewhere I could really figure out who I was without the constraints of other people’s expectations.” Miller studied at the Lee Strasberg Theatre and Film institute, the alma mater of Marlon Brando, James Dean and Marilyn Monroe, and famous for its immersive approach. “The more work that I did in class, the more I realised that there was something deeper that I loved about acting,” she says.

Shirt, Chloé; earrings, Gucci

Miller’s dream was quickly realised. She was signed by the agent Dallas Smith and, aged 21, got two parts, one in the film Layer Cake with Daniel Craig, the other in the remake of Alfie with Jude Law, filming them back-to-back. “Every single part of it was exciting,” she says. “The clapperboard, the guy calling ‘action’, movie stars and trailers and my friends coming to visit. It was incredible.” She also fell in love with her co-star, Law. The couple’s combined golden glamour was irresistible catnip for paparazzi and tabloids, so much so that Miller’s personal life eclipsed her professional one, and what had felt like the realisation of a dream became the opposite. “That happened very quickly,” she says. “The other side of it. I was so happy in my life, but it was weird, surreal. At first it was like a game. And then, very quickly, it became insidious and difficult.”

Dress and rings, Gucci

Every day, groups of men would chase Miller, trying to get her photograph, spitting at her and swearing to get a reaction. A pregnancy that she subsequently decided to terminate was announced in newspapers before she was 12 weeks gone. Her privacy was eroded and, with it, any sense of control. In response, she partied. “I was probably drinking too much, medicating in all sorts of ways, because it was jarring and scary.” Miller chose roles that seemed to intersect with her experience; tormented women crushed by fame, such as Andy Warhol’s muse Edie Sedgwick in Factory Girl. “I was desperate to have roles that were intense, to prove that I was more than a fashion plate or a girlfriend. I just wanted be taken seriously. But, really, there wasn’t much conscious decision-making. I had a decade-long case of the fuck-its. Which is kind of cool, I suppose, and intriguing, but maybe not conducive to getting your career going – ie, what I was meant to be doing.” She says she does not remember much about those years, and yet she never completely lost herself. “I don’t have an addictive personality, fortunately, and I do have a solid foundation of friends and family. So they were my saving grace.” Miller purchased a thatched cottage in the middle of a private estate in the Home Counties that offered a retreat from the mayhem. When she was 29, she got pregnant with her then-boyfriend, the actor Tom Sturridge. “I was still in the frenzy of whatever that decade had been, and it was a really grounding, incredible thing.”

The couple separated in 2015, but have remained great friends and co-parents to Marlowe, who will be going to secondary school in London in September. “She’s magical. It’s amazing when you have these little people and there’s a universe inside their heads. Her father is incredibly bright, but also very deep. And she’s straddling this kind of comedy-jokester part of me and this intensity that comes from his brilliant mind.”

Coat and scarf, Valentino; socks, Wolford; shoes, Malone Souliers

Miller had always wanted a sibling for Marlowe – “because my sister and I had always been such a team” – but was not planning on getting pregnant, particularly as she was about to start filming the first two Horizon movies. Nonetheless, the arrival of her second daughter has been a glorious surprise. “I’m in heaven,” she says, smiling. “It’s been a cathartic, healing experience, which sounds woo-woo, but it’s grounded in a way that reflects the life that I want to be living,” she says. Miller also did not intend to fall in love with Green, whom she met at a Halloween party and who, at 27, is 14 years her junior. “I didn’t expect to take it seriously and then quite quickly, I fell in love. I wasn’t like, ‘I’m gonna get a younger boyfriend.’ It was more, ‘Fuck! Why are you young? That’s so annoying.'” She was surprised, she says, by how soothing it is to be with a younger partner. “There is a difference in the way that generation of men respect women. It’s specific to him, he is very wise and well-adjusted, but I do believe it’s also that generation. They have grown up with a slightly more level playing field. I see it in his female friends as well as in the men.”

Coat, lace dress and boots, all Gucci

Miller’s own coming-of-age was played out in the Nineties, when predatory male behaviour was often dismissed as part of the system, and female beauty was considered an invitation. “I could talk myself into all sorts of shapes to make the men in the room feel comfortable. And God forbid that you offend a man’s ego by rejecting them,” she says. “It was a slightly belittling time. It’s interesting, being older now, and having been raised in that moment, learning from people who are younger about how clear they are in their boundaries, having that self-assuredness and self-advocacy, having ‘no’ in the repertoire in a way that we just weren’t encouraged to have.”

She has had, she says, a “shit-tonne” of therapy, and now, at 42, feels “much more balanced and settled and wise. I think I’ve got some wisdom from all of the things I’ve been through. The more interesting and complicated your life is, the better you’ll end up being.”

There’s no longer that need to prove herself as an actress – that work is done, which means she can turn her talents to roles that are more fun. This year, she appeared in the HBO comedy series Curb Your Enthusiasm. “I went to work and was hysterically laughing all day. I suddenly realised that’s also a version of this job, where you don’t have to go and torture yourself.” She has also started a production company and is developing her first project. “A friend of mine wrote a story based on his experiences of sexual abuse in school. It’s intense subject matter, but also really entertaining.” She would like to direct one day, and recently tried to option the book Bonjour Tristesse by Françoise Sagan. “I thought, I want to direct that, I can see exactly how I would do it, but the rights weren’t available. And they’ve now gone and shot the fucking book, which is so annoying,” she says. She’s a reader, and currently has Rory Stewart’s Politics on the Edge by her bed, having just finished The Witches, about the Salem trials, by Stacy Schiff, but Gabriel García Márquez is her favourite: “a perfect author”. She loves to cook, to entertain, have fun, be silly –”I have days where I’m impressed by my wisdom and days I am surprised by my immaturity.” She still enjoys a drink – “I like to get pissed, now and then” – although she finds it exhausting to consider how she used to party. “There’s a balance, isn’t there? It’s important to explore the edges of things, and I definitely feel I did that.”

Jacket, Stella McCartney; top and matching shorts, Dolce & Gabbana; heels, Gucci

Miller was also famous, back in her wild days, for her style: a sort of careless-yet-perfect boho-chic; floral dresses and leather belts and cowboy boots. Fashion remains important to her, and she has recently designed a summer capsule collection for Marks & Spencer that is available to buy now. “There are about 20 pieces,” she explains. “Essentially, you could pack that range in your suitcase and you have a holiday wardrobe. It’s a combination of things from my own wardrobe and things that I wanted – vintage pieces that I redesigned. It’s very much what I like to wear. I do have an aesthetic.” Today, that aesthetic is white Pepe jeans, one of her boyfriend’s T-shirts, “and a massive maternity bra!” She pulls up her top to show me, laughing.

Speaking of which, it is time for Miller to return to her daughter. I get ready to leave, pat Walter the wire-haired dachshund, who has been asleep next to me for the entire interview, and Miller returns, walking down the stairs carrying the baby, a lovely little pixie of a girl. “Do you want a cuddle? Isn’t she gorgeous?” She is gorgeous. It’s a beautiful life, forged in fire.

‘Horizon: An American Saga – Chapter 1’ is released in cinemas on 28 June, and ‘Chapter 2’ on 16 August.

The July/August issue of Harper’s Bazaar, starring Sienna Miller, is available on newsstands from 13 June.