Sam Taylor-Johnson in The Edit for Net-a-Porter

The location is a gigantic, concrete-smooth loft in New York’s Tribeca, the protagonists are legendary photographer Patrick Demarchelier and his equally illustrious muse for the day, artist and filmmaker Sam Taylor-Johnson. Standing barefoot in a crisp white cotton dress designed by her friend, Stella McCartney, limbs toned by regular running and TriYoga sessions, Taylor-Johnson looks more like a young ballerina than a 45-year-old mother of four. That she feels more at home in a director's chair, alone in her studio or at home with her husband, actor Aaron Taylor-Johnson, and her children is evident. “You're sure it doesn't look caked on?” she enquires of her makeup, concern bruising the bright blue eyes that seem to take up half her face. But it's precisely her lack of pretension, her prioritizing of intelligence, hard work and talent over connections and appearances, that has made Taylor-Johnson the force she is.

Mother to four daughters, Angelica, 15, Jessie, six, Wylda, two, and Romy, one, Taylor-Johnson was awarded an OBE in 2011 for services to the arts. Nominated for the Turner Prize in 1998, she is one of the most important contemporary female artists working today. Her first feature film, Nowhere Boy (which she fought hard to be chosen for), received four BAFTA nominations, and introduced her to her now husband who took the movie's starring role – the 23-year age gap between the two (he is 22) generating headlines and a great deal of envy. But perhaps it was her dignified divorce, from art dealer Jay Jopling in 2008, and two battles with cancer (colon then breast), both in her early thirties, that really marked her out as someone to be reckoned with, someone to be admired, someone with spirit.

Her children got her through that ordeal, she tells me later, once the props have been packed away and the sun is setting on the Hudson. “Having children has given me that sense of, 'I have to get through whatever challenges I face, because there's no option',” she explains. “People say, 'Oh, you're a survivor, you must be so strong,' but there are definitely times when you don't feel so strong. And, really, family is what kept me going.”

Home has been Taylor-Johnson’s focus since she gave birth to Wylda, her first child with her new husband, in July 2010. “I gave up [work] to build a family,” she says. “I wanted to make the rock as solid as possible, knowing that from there, I could achieve anything.” She had, she says, learned her lesson about trying to “have it all”. “When I had Angelica, I tried to do it all and it was too much. I got very sick. There was also a lot I gave up time-wise to try to prove to the world that I could do and be everything. This time around, I thought, ’I’m so lucky and so happy; enjoy every millisecond, and work will hopefully always be there.’”

And enjoy every millisecond she does, milking her precious time at home in the way that anyone who has run the working mother gauntlet for years will recognize. “I bounce out of bed to see the children in the morning, and I collapse into bed because of them at night. I love chaos, I need it to survive, and they provide buckets of it. I rarely go out. I used to feel obliged, but I have zero reason to go out – there’s nothing outside my front door that’s more exciting than what I’ve got at home.”

The family is incredibly close-knit, and she makes a point of not being apart for long. “Wherever Aaron was filming [he starred in 2012’s Anna Karenina and has just wrapped Kick-Ass 2], we’d go. Now it’s his turn to trot along behind me,” says Taylor-Johnson and indeed, he’s along for the ride today, all floppy curls and tangible energy. Tomorrow, they’re off to LA for what his wife describes as “probably the biggest, most high-profile meeting of my work life” about the next film she wants to direct. Not that she’s flustered. “I’ve been trying to land this for about a year and a half. I’ve had to fight off every big male director out there,” she says candidly. “I’ve got mood boards, casting books. No stone has been left unturned.” What’s her signature power outfit for a meeting like this? “Jeans, a pair of boots and a shirt. Really simple. It makes me feel as though I can be myself.”

She does admit, though, to a vulnerability about venturing back into her celebrity status. “Sometimes as a woman and a mother you have to fight a lot of prejudice. One New York gallerist said to me, ’Do you think you can still make artwork with four children?’ I felt my fist curl into a ball ready to sock him one. It knocked my confidence, but now I’ve got my energy back up and I’m ready to take on people like that.” Taylor-Johnson has, of course, experienced prejudice before. Those BAFTA nominations for Nowhere Boy were the perfect response to all the raised eyebrows she encountered when she was appointed director. “Making a film, coming from my background, I think there was a bit of, ’Oh, she thinks she can make a film does she?’ [Being nominated] was a real validation, it felt very powerful.”

For the awards ceremony, her relationship with the leading man the latest plaything of the tabloid press, Taylor-Johnson chose a black Alexander McQueen gown to lend confidence – “Lee”was a personal friend. "He was so wickedly naughty!” she remembers of the late designer. “For somebody so sad, he was always such good fun and such an inspiration. He was always pushing boundaries.” The trait is a popular one in those the artist is closest to. Last night, she went to see Patti Smith, another old friend, perform at Madison Square Garden. "Watching her, I just thought, ’God, you’re so wild and spirited and just out there.’ People like that inspire me, people who really don’t give a shit aboutwhat anybody else thinks, and can be creatively free. I live my life like that, too.”

It’s a rare thing to meet somebody who is quite so determinedly, triumphantly her own person – it’s no wonder she doesn’t feel the need to hide behind layers of makeup. Her glamour comes from within; everything she’s achieved in life, a reflection of her happiness and determination. And now the day is done, I can tell she’s itching to climb back into the family bubble she has built with the love of her life. For once, they have left the kids at home, so will they make sure to enjoy their night alone in the world’s most exciting city? No, says Taylor-Johnson. “We were like, ’Yay! Let’s go to New York, enjoy the hotel and actually get some sleep.”