After more than two decades on the front line of the fashion industry, and at an age at which most models might previously have been regarded as reaching (or even having passed) a suitably graceful moment to retire, 41-year-old Alek Wek is finally hitting her stride. “The party’s just getting started,” she tells me, flashing her trademark gap-toothed grin. In January this year, she landed her first solo Vogue cover (in Ukraine), and was shot for a further 10 glossy covers last year, including UK Elle, Paper, Dazed and Pop magazine. “They never thought I was Pop material before,” she says.

The things I used to worry about are now things I love about myself

And hard though it may be to believe, given that the South Sudanese-born supermodel has walked the runway for every major fashion house including Chanel, Givenchy, Marc Jacobs, Yves St Laurent and Gucci since her breakthrough in 1996, she feels that mainstream commercial campaigns eluded her… until now. This month she is featured in a new campaign for US clothing store Ann Taylor. “You don’t get more mainstream or typically American than that,” she points out. She also appeared in campaigns this autumn for Theory and Kurt Geiger. “To see diversity finally kicking in and being embraced is amazing,” she says. “We’re not there yet – there’s still some way to go, but…” She trails off, holding her long arms up in an expression of exhausted relief.

Facebook Twitter Pinterest Alek wears emerald green dress with twisted top in soft crepe wool and tailored bolero jacket, both by Clare Waight Keller for Givenchy, givenchy.com. Photograph: Jody Rogac/The Observer

We’re in the café of a studio complex overlooking the Hudson River in Manhattan’s Chelsea, which contains the very studio where Wek was first shot by Steven Meisel, as part of a story for Italian Vogue in 1996. “I hadn’t seen anybody that interesting, that black and that beautiful in a long time,” he later said. A year on, Wek became the first African model ever to appear on the cover of American Elle. “But I had to really fight for it,” she says. There was a misconception that darker-skinned African women didn’t sell magazines, but Wek’s cover prompted a huge response. Oprah said that if Wek had been around when she was growing up, then she would have felt beautiful, too. But it would be another 20 years before the same magazine would put another African model, Angolan Maria Borges, on its cover in 2017.

I find younger men much more interesting. They have less baggage

Alongside the recent impressive roster of cover shoots and campaigns, Wek’s also been branching out into acting, with a small role in the film Suspiria, a supernatural horror flick and a remake of the 1977 film of the same name. Wek was recruited by the film’s director, her longtime friend Luca Guadagnino, and she plays Miss Millius, one of a coven of witches controlling a dance academy, alongside Dakota Johnson and Tilda Swinton. “When I saw that Tilda Swinton was going to be in it, and heard that she wanted me for the role, I was so nervous,” admits Wek. “But she’s so cool, and so real, and so normal.”

The film was shot in an old hotel in Lake Como. “It’s not like fashion – you go for months on these shoots,” she says, still looking shocked. “It was good to challenge myself and deal with all those different personalities, for all that time.”

Facebook Twitter Pinterest Alek wears Elise dress by Roksanda Ilinčić, roksanda.com. Photograph: Jody Rogac/The Observer

She herself is chatty, irreverent and lively – “I am such a strong personality, but I’m really soft as well,” she says – and bounces from subject to subject enthusiastically, if somewhat haphazardly. Her accent similarly darts about, at moments carrying an African inflection from her motherland, before becoming pure Hackney, where she landed as a refugee, then sliding into Americanisms picked up in New York, her home for much of the past two decades.

These days, she lives in a brownstone in Fort Greene, Brooklyn, with her fox terrier, Little Bit. But tomorrow she’ll be back in London to co-host (with Jack Whitehall) the British Fashion Council’s annual Fashion Awards in partnership with Swarovski at the Royal Albert Hall. “I’m really honoured to be asked, and to be doing it in London,” she says. “That is where everything started for me. That’s where I came of age and where I felt like it was OK to be Alek. And it was where I felt I didn’t have to keep running. Coming from civil war, as a refugee, you are always running.”

Wek was the seventh of nine children. Not only was there no access to TV or fashion magazines, the family’s two-bedroom home did not even have running water. But her parents valued education. Her father, Athian, worked for an education board, and insisted his children were all educated to a high standard, speaking Arabic in school as well as their native Dinka. She paints a relatively idyllic picture of her early years. “We’d run up the hill to spot planes, and we’d take the cows to eat grass, trying to stop them eating the neighbour’s peanuts,” she laughs.

Facebook Twitter Pinterest Alek wears red lace cross front cami top and belted front pleat trousers both by Victoria Beckham, victoriabeckham.com. Photograph: Jody Rogac/The Observer

The outbreak of a bitter civil war when she was nine shattered the peace. “I vividly remember asking my parents: ‘Why do we have to leave? Why is the whole town burned down?’” she says. “Militias would come in the middle of the night, and you’d hear screaming and shooting and, the next day, people had disappeared.” She has described smelling rotten bodies in the streets. “The police ran out of ammunition, and could no longer protect us, and that’s when we realised we just had to go. Nobody can comprehend what we went through,” she says, without self-pity. Her experiences continue to inform her commitment – Wek has worked with the United Nations High Commission for Refugees since 2012, and with Unicef to highlight the continuing violence in South Sudan.

The family scratched a survival in the bush, alongside other refugees fleeing the violence; several of her siblings contracted malaria, and her father became ill from an old hip operation which became infected during the long walk. He died at the home of a relative in Khartoum. Wek was 12. Her mother was now a widow, with nine children.

“At the time, I didn’t really understand the impact on her,” says Wek. “Now, I understand how unbelievably hard it must have been.” And what, I ask, was the impact of losing her father? “It would have been nice to have him around,” she nods, stoically. “Sometimes when I accomplish things, I think, my dad would be proud – it would be nice if he could be here.”

Facebook Twitter Pinterest Alek wears black and red Chinese flower padded jacket by Simone Rocha, simonerocha.com. Photograph: Jody Rogac/The Observer

At 14, Wek arrived in London as a refugee, accompanied by two of her sisters, but without their mother, who followed two years later, after recovering from typhoid. “My mother is so resilient,” she says. “That’s one of the things she’s passed on to us.”

Wek moved in with an older sister and young nieces in Hackney. “I was just like, ‘What is this place? Where am I?’ It was bloody cold,” she says. “But I threw myself into everything. I learned to swim, ride a bike, ice skate. I was the number one triple-jumper,” she says proudly. At 5ft 11in, with legs for days, it’s not hard to see how. Those legs were also spotted by a model scout in the unlikely environs of a Crystal Palace market, when Wek was 18. In the middle of an art foundation course, with plans to study painting at Central Saint Martins, she’d never considered modelling. Plus, her mother was firmly against the idea. “She said, ‘Absolutely not, you’ll go to college and get your degree, my daughter,’” she recalls. “But which girl wouldn’t want to play dress-up at 18?”

While she dutifully finished her foundation course, she was cast in Tina Turner’s video for the James Bond film Goldeneye, then flew to New York for the summer in 1996, to test the waters. “I was planning to go back and start university in September,” she says. Instead, Ralph Lauren booked her to open his New York Fashion Week show that month, as did Donna Karan. And Calvin Klein booked her to close the show. She never made it to Central Saint Martins.

Facebook Twitter Pinterest Alek wears flare hem striped dress, heart belt and pointed lace up boots all by JW Anderson, j-w-anderson.com. Photograph: Jody Rogac/The Observer

It was not, she admits, a seamless adaptation to the heady world of high fashion. She wanted to turn down an early shoot with the legendary Herb Ritts, for the Pirelli calendar. “I had to be naked, and I was a virgin, and I was just, like, ‘No, we’re not doing that,’” she says.

“My agent took me to one side and said: ‘He is not a pervert, and he’s not going to be weird. He is an absolute professional, and if anybody disrespects you, he will throw them out himself.’”

But, given the revelations in the fashion world about the extent of the exploitation of models by photographers and agents, sparked by the #MeToo movement, are there jobs she wishes she had said no to?

She gives me a dramatic side-eye, and takes a deep gulp from her glass of water. “You have no idea,” she says. “It’s not just a sexual thing – it’s about bullying. You have a lot of young people in an industry making lots of money for adults, not all of whom care about them.”

Facebook Twitter Pinterest Alek wears knitted merino wool face skirt by Matty Bovan, matchesfashion.com. Photograph: Jody Rogac/The Observer

There are jobs for which she did put her foot down. She tells me stories of being on a snow-covered mountain in Switzerland, in a bikini. “I was not catching pneumonia for fashion,” she says firmly. And of being in an abattoir, surrounded by huge joints of refrigerated flesh. “They’re not going to get a good picture if I’m cold.”

“You see this?” she says, running her finger in a circle in front of her face. “This is all woman. This is not a little girl. I know what I am doing.” She feels differently about nudity now, too. “I will show my body, but I wouldn’t show it like I would when I was 20,” she says. “I feel beautiful, and I’m comfortable with myself – much more than I was in my 20s. But I feel you have to have something for yourself.”

“How I carry myself is different now,” she continues. “And what makes me sexy is different now. The things I used to worry about are now the things I love about myself and make me who I am.” Her dentist wanted her to get braces. “I’m like, ‘No.’ People have gaps and gaps are sexy now, anyway.” Her doctors wanted to break and reset the little finger on her right hand, which is slightly malformed. “I was born with it – it doesn’t hurt,” she says. “These are the things that make us interesting, the things that make us beautiful.”

For the past 20 minutes of our conversation, her phone has been pinging constantly, and Wek has been politely glancing at her screen, but not responding. I tell her that it’s no problem if she needs to. She breaks into a giddy grin. The texts, it turns out, are from a new love interest.

“I’m single and I’m ready to mingle, but I like this one,” she giggles. They met very recently, at a backyard party in Brooklyn; he’s a trainee lawyer. “I don’t want somebody in this business. I need somebody who I can talk about normal, everyday life,” she says. He’s also a decade younger than her. “I find younger guys much more interesting, because the older they get, the more baggage they have,” she muses. Wek would like to have children, she says, and feels as if she’s finally ready. “In my 20s, I had to go off and do my thing. I felt like I had to grow. I didn’t want to have babies and feel like I didn’t reach my potential.”

Many in her position might feel that literally changing the face of fashion would mean they’d now reached it – but not Wek. “I can be choosy about which jobs I do now, and I can take care of myself,” she says. “And I like all that, but I have another chapter, and I still want to evolve.’

Alek Wek co-hosts the Fashion Awards, in partnership with Swarovski, at the Royal Albert Hall, London

Makeup by Linda Gradin at Latelier NYC using MAC. Hair by Fernando Torrent at Latelier NYC using Leonor Greyl. Model Alek Wek at Storm. Fashion assistant Penny Chan. Photographer’s assistant Justin Mulroy