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Specifically, precisely, what Taylor-Joy wants to communicate is that her happiest place on earth is a film set where she’s covered in grime and, with any luck, some kind of prosthetic blood, and where someone is challenging her to do something that’s physically hard so she can ignite the competitive spirit within herself and see how much she can endure. And that particular day in Iceland checked all those boxes, with the bonus of getting to swim around in the freezing North Atlantic. A very good day, indeed.

But this is a young woman who likes to get dirty, so much so that when she was making the new David O. Russell film earlier this year, and she met the man who created her favourite brand of fake blood, who revealed this fact as he was applying the fake blood to her body, well, she just lost her mind. “I live in your blood! It’s my favourite kind of blood! Thank you thank you thank you!”

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“I thought, ‘Who’s that girl?’” Kidman remembers. “Then I take another look and, ‘Oh, that’s Anya!’ She’s in the mud, dressed in nothing, it’s freezing cold and the wind’s whipping around, and it was like meeting a kindred spirit. This is my kind of girl!”

Right now, Taylor-Joy, 25, seems to be everyone’s kind of girl. Her schedule is booked solid for the next two-and-a-half years, starting soon with The Menu, a dark comedy set in the world of exotic culinary culture directed by Mark Mylod (Succession) and then moving next year to Furiosa, George Miller’s prequel to Mad Max: Fury Road.

After that, she’ll reunite with Queen’s Gambit writer-director Scott Frank for the thriller Laughter in the Dark and Eggers again in a reworking of the vampire classic Nosferatu, the latest collaboration in a partnership that began with her first “real film”, the unnerving 2016 horror movie The Witch.

“All my friends are always like, ‘What are you doing? Take a break,’” Taylor-Joy says. “But the roles are too good. I wouldn’t be able to deal with it if I didn’t say yes. I wouldn’t cope. I’d rather just go for it and do my best.”

I wonder, though – and, who am I to say, I’ve only known her for all of an hour now – who are these friends telling her this. Within five minutes of meeting, we’re talking about the home she recently bought, which leads Taylor-Joy to share something from her past that always bugged her.

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People would ask her, constantly, “Where is home?” And depending on her mood, she’d answer, “Wherever I’m sleeping that night, I make home,” or maybe “Home is the people I love.”

Those answers usually weren’t acceptable and, not only would they get under her skin, people’s reactions would make Taylor-Joy feel like there was something wrong with her in not being able to fulfil the expectations inherent in that question. Now she doesn’t care. And she’s damn well not going to be feeling bad about it.

“My third movie was Split, with M. Night Shyamalan, and he and I got very close,” Taylor-Joy says. “And I remember him asking me one day, ‘Are you running toward something or running away from something? Which one is it?’ I think I’m running toward something. There was the moment when I was 19 or 20, and I felt very confused just because I’d poured so much energy into characters, that I didn’t know who I was any more. But through quarantine and then the months that have followed, I just like to feel useful. I don’t feel like I’m leaving myself behind as much any more.”

Where Taylor-Joy feels most useful is the set, where she naturally assumes the role of carer and advocate. On The Northman, she took on the unofficial job of “cold cheerleader”, arriving for work every day proclaiming, “Isn’t this amazing? I know we’ve been in the ocean for hours and it’s so cold we all want to cry! But we’re making art!” (“I’m surprised someone didn’t throw me to the ground at one point,” Taylor-Joy says, laughing.)

She does this on every one of her projects, making sure everyone feels safe and sound and supported and loved. (“She seeks people out,” says Queen’s Gambit executive producer William Horberg, likening her talent to Cate Blanchett’s.) Taylor-Joy thinks this caregiving instinct comes from feeling unheard and unseen as a kid, a time when she was bullied in her self-described awkward years growing up in London.

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“My favourite situations are when people are self-described weirdos and they feel comfortable,” Taylor-Joy says, letting out a contented sigh. “That’s all I want to do: make people feel like whatever they’re bringing to the table is a beautiful expression of their originality.”

Taylor-Joy has spent the last few months living in Los Angeles, a place she’d never felt comfortable in. But now, having explored the canyons, she says she has found her pocket, a place she “can connect with and plant something and it will grow and bear fruit, if that makes sense”. Driving home one night from shooting the untitled Russell movie earlier this year, listening to some good music – it might have been Florence and the Machine or Kate Bush or Elliott Smith – she felt like she was going home, a far cry from when she first came to the city at 18 and, filled with anxiety, remained holed up in her hotel room.

She’s working, even when she’s not on set. Lately, Taylor-Joy has been learning how to drive a car like a badass so that she can do most of her own stunts in Furiosa. She’s a bit dodgy on the details (“I’m trying not to get in trouble!”), but it’s OK to say that she’s enjoying learning high-octane manoeuvres under the tutelage of Miller’s stunt team.

She also keeps filling journals with her own thoughts and those of characters she’ll be playing, along with lyrics to songs she’s writing. Melodies have long coursed through her head, and she really got into making music while shooting The Northman, layering vocals on top of vocals to create some “pretty bizarre” songs.

“I’m very big into lyrics,” Taylor-Joy says. “My favourite music makes you think. I put a lot of thought into that, and that’s usually the aspect that makes me feel better. It’s the cathartic release when you look at a song and a poem and go, ‘Oh. That’s what that situation was.’ It’s not this amorphous cloud that I’m trying to understand.”

One of her journals, the one she kept while shooting the Russell movie (she’s sworn to secrecy) contains the long, red acrylic nails she wore in the film (“that sounds gross, and I don’t care,” she says). Taylor-Joy keeps a memento from every character she plays. From The Queen’s Gambit, she has a hat, a couple of pairs of shoes and some really great pants that she can actually get away with wearing in her day-to-day life. As she wrapped The Northman, Eggers gave her a sword, knighting her with it as he presented it.

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“I do love beautifully crafted weapons, especially from a film set that have a meaning behind them,” Taylor-Joy says. “I was like, ‘Really? I get to keep this?’” Her next thought: “Please don’t tell me I have to travel with this sword.” Eggers shipped it to her London home, the one that she never sees, where it will someday be mounted on a wall. She’s OK just knowing it’s there.

Meanwhile, work calls. Picking through her cold In-N-Out grilled cheese, Taylor-Joy circles back to that conversation she had with Shyamalan. “I’m definitely running … I’m under no misguided thought that I’m taking a leisurely stroll anywhere,” she says. “Oh, no. I’m running. It’s a concerted effort. But it just fills me up so much. It makes me so happy. And I feel so lucky that I wake up at 4 o’clock in the morning and think, ‘I get to do this today!’”

Then she goes to work. And she arrives home.