Dafne Keen does not much look like Lyra Belacqua, at least not as Philip Pullman describes her in His Dark Materials. In Northern Lights, the first book of the trilogy, she is “like a half-wild cat”, with dirty fingernails, green eyes and grubby blond-ish hair. Keen, who is half British, half Spanish and lives in Madrid, is darker and is already the master of an intense glare, as anyone who saw her alongside Hugh Jackman in the Wolverine swansong Logan will know. When we meet, in a London hotel, she has the self-possessed cool of a total pro, even at 14. But there are plenty of Lyra-esque flourishes that make it obvious why she got the part.

She was almost 12 when she finished filming Logan. She had heard about the BBC/HBO adaptation of His Dark Materials, then in its early stages, and sent in an audition tape. But she didn’t hear back. “I thought, never mind, I’ll just carry on with my life,” she says. “Which is when I got stung by the jellyfish.”

The production team had finally replied, asking her to make another tape. Keen was on holiday in Puerto Rico. “I thought, right, I’m going to have a chilled-out swim and then I’m going to get ready. I suddenly felt this thing on my face and then it started stinging and then it expanded all over my face. I ran to my mum and I went, ‘Mum! Is it really red?’ My mum went, ‘No it’s fine.’ And then she went, ‘Oh no, it’s not fine.’” Her face was red and swollen but she had to do the tape. “So my audition is with a jelly-face,” she smiles.

The next step was to meet Ruth Wilson, who plays Mrs Coulter, one of the best evil characters in children’s literature. “I was sitting in the waiting room with 20 other girls,” Keen remembers. “I was thinking, oh god, they’re all blond. I don’t physically look like this character, and these girls all do. I went in, shook hands with Ruth, and five minutes later, she looked at me and said, ‘You know, you have the same eyebrows as me.’” Fans of the books will know that this is a big thumbs up. Days later, she began rehearsals, with Wilson and puppets. In Pullman’s books, people have daemons, an animal manifestation of their “inner self”, which lives alongside them. Because the daemons on screen are CGI, the actors shot their scenes with puppets to make their interactions as authentic as possible.

When Philip Pullman writes, he isn’t trying to bring down the church, he’s bringing down the system

Naturally, Keen is practised at describing what her own daemon would be, were this world to have daemons in it. “Mine is quite easy to figure out, because it’s what everyone called me on set. Everyone calls me Monkey.” In the books, daemons change form until their human reaches adulthood, when they settle as one fixed animal. Keen particularly liked hers as a pine marten.

We meet the morning after the world premiere of His Dark Materials, which was the first time Keen had watched it. “Everybody had seen it apart from me! I’m really busy filming season two, so I had no time to watch it. I had Philip Pullman right next to me, and I was like, oh god! But I think he liked it.” Did he offer his approval? “His wife came up to me and was really lovely and was saying I was the perfect Lyra. I was really happy to hear that.”

Dafne Keen as Lyra in His Dark Materials. Photograph: BBC/© Bad Wolf/HBO

Keen had not read the trilogy before she auditioned. “Now I’m a massive, massive fan. As soon as I read the books, I knew this was a good message to the world, and it’s important that we have stories about young girls, because there aren’t many,” she says. At the premiere, Jack Thorne, who wrote the screenplay, likened Lyra to Greta Thunberg. Though she does not know it, the future of the world rests on Lyra’s shoulders, and she has to fight tooth and nail to defeat the forces that wish to suppress free will and independent thought. Keen approves of the Thunberg comparison. “I am genuinely in awe of that girl.”

There have been various adaptations of His Dark Materials over the years: a Radio 4 series, a play at the National Theatre and the 2007 Hollywood attempt, The Golden Compass, with Nicole Kidman and Daniel Craig. It was supposed to be a trilogy, but only the first was made – and Pullman’s theme of an abusive authoritarian religious body was watered down almost beyond recognition. The television series seems more comfortable with its source material, and its Magisterium, the governing body of the Church, is portrayed as a fascist regime.

In 2007, the Catholic League called for a boycott of The Golden Compass, despite the religious references being excised, and the Vatican also denounced the film and Pullman’s writing. Keen had seen it – was she aware that this new version might be controversial, given the backlash the movie attracted? “I thought that was sad, but I understand why they had to do it,” she reasons, diplomatically, of the decision to soften the book’s themes. “But I think people are reading too much into it. When Philip writes about the Magisterium, he’s not bringing down the church, he’s bringing down the system.”

Mutant to mutineer … with Hugh Jackman in Logan Photograph: Allstar/20th Century Fox

Keen was born and raised in Spain and is bilingual. Her mother María is Spanish, and as well as being her acting coach is also an actor, as is Keen’s father Will. He has a part in His Dark Materials, as Father MacPhail, part of the Magisterium faithful. “He is terrifying,” says Keen. “He always plays bad people. I don’t know why because he’s so nice. I genuinely think it’s because he’s bald and has green eyes.” She practically grew up in a theatre rehearsal room, because of her parents, but she thought she would be a biologist, like David Attenborough. “Then I found out you have to study biology, and to do that you have to study maths, and I went, mmm no, I’m not doing that. I hate maths so much, you can’t even imagine.”

A friend of her mother’s was making a short film, and needed a child for it, so Keen gave acting a go. She loved it. She did a series in Spain, The Refugees, alongside her father. (“He was playing my evil father, yes. Always got to give it the psychopathic twist.”) She picked up an agent, who put her forward for Logan, and she got down to an audition with Jackman. “In the waiting room, once again, there was this perfect LA beautiful blond girl. I was just, like, a small, scrappy Latin girl. I always think it’s not going to work out for me, and then it went really great.” She auditioned with Jackman, then asked if she could try again, only this time she said she’d like to improvise the scene. She was 11. “My heart was beating big time,” she says. “I thought, I’m just going to dive in and ask them, and they loved it, so I was lucky.”

Jackman remembers the audition well. “[Director] Jim Mangold looked at a lot of actresses for Laura. When he told me about Daf, I was hopeful, but when we tested together, I was blown away,” he says over email. “She was every inch Laura. When Jim asked her if there was anything more she wanted to show us, she said, ‘Can I improvise?’ That’s the actor that got the part and who you see on screen.”

“Hugh is the nicest human being,” she grins. “I used to call him the human jukebox because he was always singing. Lin does the same thing.” Lin is Lin-Manuel Miranda, who plays Lee Scoresby in His Dark Materials. He got Keen tickets to see his smash-hit musical, Hamilton. “Two VIP Lin-Manuel Miranda guest tickets. I felt like such a diva.” On set, she would find herself singing the songs from it, but was too shy to sing when he was there. When Miranda had finished shooting, they all went for a meal to see him off. The bartender recognised him, and put My Shot on the stereo. “Me and Lewin [Lloyd, who plays Roger] were like, we’re not throwing away our shot, we’re singing this song.” They all joined in. “I’ve got videos of me and Lin singing it.”

Right now, Keen is preparing to go back to Wales to film season two, which loosely adapts The Subtle Knife, the second book in the trilogy. The third season, which will take on the astonishingly ambitious The Amber Spyglass, may take a little longer to pull together. Still, she is happy to live as Lyra for a while yet. She has taken plenty of her away from the experience already. “She taught me to speak up. Be bold, be brave, be yourself. Don’t follow rules, because rules can be useful, but they can be very stupid and pointless,” she says – sounding very much like her Lyra herself.