Francesca Hayward groans as she climbs the stairs, half hidden behind the black net tutu she is carrying. She’s tired after a morning’s rehearsal, and her legs are grumbling about the vertiginous climb to the room at the top of the Royal Opera House where we are meeting. If it seems strange that a ballerina should struggle with a staircase, that’s an indication of just how hard she is currently pushing herself. Hayward is a dancer who has reached the top and is determined to explore every view it offers.

She is already familiar to dance lovers as a principal of the Royal Ballet, who this season has been the most devastating Manon since Sylvie Guillem, and a heart-rending Juliet. She has brought poise and radiance to Aurora in The Sleeping Beauty and is about to star as the mischievous heroine in Coppélia, the part that is causing her such aches and pains to learn. “It’s relentless, stepwise,” she says. “She never stops jumping around with all her friends. I want to say, ‘Why don’t you have a rest? Stop showing off!’”

She giggles. Humour and warmth run through any time spent in her company. So do quiet good sense and a wariness of assuming too much: qualities she is going to need in abundance, given the sudden celebrity that is bound to arrive thanks to her leading role in the film version of Cats. Its internet-breaking trailers, listing familiar names such as Judi Dench, Jennifer Hudson, Taylor Swift, Idris Elba and James Corden, end with the phrase: “And introducing Francesca Hayward.”

“Why don’t you have a rest? Stop showing off!”

The result of this is that “Who is Francesca Hayward?” is now the most searched term on Google for her name. She laughs again as she points this out. “It’s very funny.” Is she ready for the mayhem that may accompany the film’s release? “Honestly, I don’t know what to expect. I am really taking each day as it comes. I am a principal at the Royal Ballet. That was what I have striven for my whole career. I didn’t feel this would take away from that, I’d only gain more experience. I’ve got nothing to lose.”

The first time she glimpsed herself as Victoria, a cute little cat, was when she saw the trailer on holiday in Mexico. “I hadn’t seen myself with fur until the day the whole world saw me with fur!” she says. “I just stayed in the hotel lobby and watched it over and over again, because it’s a lot to take in — it’s you, but your ears are furry and you have a tail. It’s all a bit bonkers.”

At the world premiere of Romeo and Juliet: Beyond Words, in London.

Yet she wasn’t as shocked as the rest of the world by the female cats having breasts. “I find it funny that people are funny about that — if you’ve seen the stage production, it’s the same.” The row about how she, as a performer of colour, has a white cat face was something she was more prepared for, “because that is a sensitive subject these days”. But her answer to the critics is unambiguous. “Obviously I would never have agreed to be a part of something that would try to change the colour of my skin had I been playing a human. For me, the bottom line is, I’m playing a cat. There is no more discussion. I am a cat that’s white, let’s not read into it.”

Hayward speaks directly, calmly and without hesitation. She is getting used to speaking out on such themes. Earlier this year, she was one of the 15 women, alongside the climate activist Greta Thunberg, the model and mental health campaigner Adwoa Aboah and the author Chimamanda Ngozi Adichie, chosen by the Duchess of Sussex as “forces of change” and photographed for the cover of Vogue.

“I am a cat that’s white, let’s not read into it.”

“That was a pinch-me moment, because I had been buying Vogue ever since I was very small,” Hayward says. “When I was training at the Royal Ballet school at White Lodge, I never did my homework, and apparently — I don’t remember this — I would have a copy of Vogue inside my maths textbook.”

She didn’t meet the duchess, but they did speak. “I was in an Indian restaurant with my auntie when Edward Enninful, the editor, rang me and said someone wanted to speak to me,” she recalls with a grin. “It was really noisy, so I had to go outside. So I was on the street in Covent Garden and talking to Meghan Markle. It was really surreal.”

Hayward, at age 10, the 2002 Best Young Ballet Dancer on Britain’s Brilliant Prodigies.

She felt proud to be included: “I hope people take inspiration, not from the fact that I am mixed race, but from the fact that I don’t want to be labelled any more, because I find that a bit tedious now. It’s not that I am not proud, I would just like it to get to the point where we can stop asking those questions, because they seem irrelevant to me. It’s not something I ever focused on.”

The daughter of an English father and a Kenyan mother, Hayward was brought up by her grandparents in Worthing, West Sussex. She has a strong relationship with her father, but it is her grandparents to whom she still speaks every day. They guided her career, not least by letting her watch ballet videos, which she copied obsessively. The Royal Ballet has grown increasingly diverse, but she is its first mixed-race female principal.

It never occurred to her that a career in ballet was not for her. “I never had a moment of feeling ‘different’, in inverted commas. I always worked my hardest, and felt treated and judged according to my potential. In this company, if you’re bringing some joy or light to the stage, you’re welcome.”

The Royal Ballet has grown increasingly diverse, but she is its first mixed-race female principal.

In fact, it was the calibre of her talent that marked Hayward out. She is surrounded by a remarkable generation of dancers, but her dramatic intensity and lyrical grace, her quicksilver movements and ability to inhabit a character in all its depth and detail, make her stand out.

“When you write all these mad stories on paper — Swan Lake is a prince who falls in love with a bird — it’s ridiculous,” she says. “But there’s a way to tell it, to wrap everyone up in it so they stop asking questions and are completely absorbed. I love making things as real and natural as possible. If you give it full commitment and belief, the person watching will believe as well.”

The film of Andrew Lloyd Webber’s Cats, directed by Tom Hooper, offered different challenges. Hayward not only leads the dancing, but sings — a song specially written for her by Lloyd Webber and Taylor Swift. “It was a mad experience from start to finish and it was not how I thought it would be.”

Hayward in rehearsal for Alice in Wonderland at the Royal Opera House. Dancer Nicol Edmonds is behind.

Singing was undoubtedly the most nerve-racking part of the filming. Hayward jokes that she became “such a diva”, trying to protect her voice with special food and ginger tea. “I wouldn’t do it for dancing — I am pretty laid-back,” she giggles. She feels proud that she pushed herself out of her comfort zone, but found filming testing.

“Looking back, I don’t think I could have coped with it if I didn’t do the job I do, and if I hadn’t had all the training ingrained in me to cope with this kind of pressure,” she says thoughtfully. “I felt quite lost. Though I was gaining so many other things, there was a big part of me that was still …” She pauses. “Neglected, maybe. It felt like it was missing. I think I am a stage animal. I obviously loved filming, but it’s not the same feeling as being on stage — no adrenaline and sometimes not the same atmosphere. But that was a great learning tool for me on how I had to create my own feeling, my own atmosphere.”

A song specially written for her by Lloyd Webber and Taylor Swift.

She found it fascinating, too, to watch actors such as Dench, Elba and Hudson at work. “I had to try not to put them on a pedestal and freak out about them,” she says. “I was expecting some huge egos and foresaw that maybe we’d have some tense days on set. But it was the complete opposite, and that’s quite a miracle, I think.”

Her new fame outside the Royal Ballet hasn’t affected her sense of being part of a team inside the company. She pauses the interview when we hear the famous Tchaikovsky music for the Rose Adagio streaming over the speakers; we sneak into a box to watch first soloist Anna Rose O’Sullivan make her debut as Aurora, standing perilously en pointe as her four suitors hold her hand. Hayward watches intensely, her hand moving slightly in time to the music. “After that, by the time you get to the rest of the ballet, you’re so tired, you can’t stress about it,” she says. “I’ve been trying to give her the best tips, not about steps, but about how she will feel exhausted and want to give up, and that’s OK.”

Hayward with William Bracewell in Romeo and Juliet: Beyond Words.

Cats isn’t Hayward’s only big film role this winter. She is also playing Juliet in a version of Kenneth MacMillan’s Romeo and Juliet, shot on location near Budapest, starring dancers from the Royal Ballet and directed by Michael Nunn and William Trevitt, collectively known as the BalletBoyz. After a limited cinema release, it will be shown on BBC2 over the holiday season.

It reveals Hayward both as a luminous screen presence and as an astonishingly lyrical, heartfelt Juliet, a dancer who illuminates the traditional steps and makes them live and breathe. She felt being on location deepened her portrayal — which was reflected when she returned to the role on stage.

“It was an amazing experience. I’ll never forget leaving the set in Budapest, late at night, and feeling really emotional, as if I were leaving Verona as I knew it. I could walk past the places where I fell in love, where I had my first kiss. It was so real. It totally transformed the way I thought about Juliet.”

She believes the two films arriving together is perfect timing, that one enhances the other. “With Cats, I am proud to have done it, to be singing and doing different styles of dance. But maybe, when people ask ‘Who is Frankie Hayward?’, well, Romeo and Juliet is me saying, ‘Let me show you. This is kind of what I do.’”

Romeo and Juliet: Beyond Words is in select cinemas from December 16, and on BBC2 over Christmas. Cats opens on December 20