One morning last August, Anna Wintour was playing tennis with her coach in the 40-acre grounds of her Long Island summerhouse. She noticed he seemed a little distracted: “But his wife was about to have a baby, so I thought he was nervous about that.” Then it struck her that they had attracted an unusual number of spectators. The house was brimful with family, but it was earlier than most people get up on a weekend. (“I’m a morning person,” says Wintour, for whom anything later than 5am constitutes a lie-in.) As she prepared to serve, she heard a car pull up. “I am pretty OCD about guests and where they are sleeping. I thought, I’m not expecting anyone else, I don’t have any more rooms. Who is this? And then I thought – that looks like Roger [Federer, with whom Wintour is good friends]. And that looks like [his wife] Mirka. And that looks like their twins.” Wintour’s daughter Bee Shaffer, it transpired, had arranged for a Federer-Wintour family tennis tournament, “which was the best gift a daughter could give a tennis-mad mother. I got to play doubles with Roger for the first time in our very long friendship, against my two nephews.” Twenty-five floors above Manhattan, behind the ebonised mahogany Alan Buchsbaum desk from which she has ruled the fashion world for three decades, she leans back in her chair and smiles at the memory. “We won, of course.”

Anna Wintour, the editor of Vogue, goes over page layouts at the magazine’s offices in New York, 2003. Photograph: Joyce Dopkeen/New York Times/Redux/eyevine

Of course. Anna Wintour plays to win in everything she does. She is editor-in-chief of American Vogue and artistic director of parent company Condé Nast, but her job titles do not come close to describing her iconic status. Vogue has been a launchpad from which she has powered herself to become a player in culture and politics. She is a fashion industry kingmaker, a Washington insider (Barack Obama’s fourth-biggest fundraiser in the 2012 campaign), an art world luminary (the Costume Institute at the Metropolitan Museum was renamed in her honour in 2014) and a Dame of the British Empire. And her haircut alone – as preternaturally unruffled and impenetrable up close as it looks in photographs – is recognisable from space.

The Anna Wintour mythology is as much about power as it is about fashion. It owes a great deal to the 2006 film The Devil Wears Prada in which Meryl Streep’s ice-queen editor, assumed to be a cartoonised Wintour, created a character that popular culture has thrilled to ever since. Such is her fame that a mere rumour of her departure is enough to send shockwaves through the fashion and media worlds. (Last summer, these rose to such a clamour that Condé Nast issued a statement confirming Wintour would remain at Vogue “indefinitely”.)

Her office has an air of ambassadorial gentility. No industrial styling, no modish succulents. Definitely no treadmill desk. The south wall is glass, diffusing the room with silver light bouncing off the towers of the financial district. Framed photos of her son Charles and Bee, as children and as the thirtysomethings they are now, are prominently displayed on her desk, on the window ledge and between a pair of topiaried miniature trees standing sentry on the limewashed sideboard. A cornflower-blue ceramic vase is filled with fresh ranunculus in Titian reds and coppers; a glass pot holds sharpened HB pencils. Only the lipstick mark on the grande Starbucks coffee cup and the Chanel sunglasses in the in-tray give the Vogue game away.

Wintour sits next to Caroline Rush, chief executive of the British Fashion Council, and the Queen on the front row at Richard Quinn’s show, London fashion week 2018. Photograph: WPA Pool/Getty Images

I am summoned to this inner sanctum 10 minutes before our scheduled 9am interview time. Wintour is wearing a calf-length Erdem dress in dark silk with a bright floral print, collared with two sparkling necklaces. A blush pink coat and a jade green scarf are thrown over a corner chair next to a small Victoria Beckham black leather tote. With characteristic briskness, she has already wrapped her portrait shoot with Tyler Mitchell, who last year became the first black person to shoot a Vogue cover when he photographed Beyoncé for Wintour’s September issue. “He’s charming, he’s intelligent – I’ve been impressed by what he’s said yes to, and what he’s said no to,” she says of Mitchell. “Also, he’s quick.”

Before the shoot, she was watching Andy Murray’s match at the Australian Open on television – his first after announcing his retirement. “So emotional,” she says, gravely. Is it true that she herself plays tennis every day at 5am? “I don’t play tennis as much as I used to, but I get up every day between 4am and 5am, and I work out every day.” (Her game is, she says, “terrible! But I enjoy it.”) While we’re on the subject, this seems an opportune moment to verify some of the other Anna Wintour myths. What about spending only 20 minutes at parties? “Well, it depends on the party. If it is fashion week, then most likely I will be in and out. But there have been many times I have stayed a lot longer, believe me.” She is smiling, but her folded arms semaphore impatience to change the subject. I am sorry to say that I chicken out of asking her if it’s true about eating medium rare steak for lunch every day.

Edna Mode from The Incredibles bears a clear resemblance to Wintour. Photograph: Imagenet

Becoming a public figure in a way no other Vogue editor ever has been “wasn’t a conscious path”, she insists. “I don’t work for Anna Wintour, I work for Condé Nast. I don’t have any kind of social media accounts or look for personal recognition.” But Wintour is instantly recognisable, thanks to a style that has remained almost unchanged since the 80s. Her sleek bob teamed with a sharp wit has often been a power combination, channelled by Uma Thurman as Mia Wallace in Pulp Fiction, by the diminutive Edna Mode in The Incredibles and by Taylor Swift at her most sassy. But the style was “not a strategic decision”, Wintour insists. “I feel comfortable with it, that’s all. I am a creature of habit. Honestly, Jess, it’s not something I spend any time thinking about at all. I come to the office and do my job.”

Wintour’s image of cool, impermeable authority has become a blueprint for successful female leadership. I am sure I even caught something of Wintour’s staccato delivery in the sardonic crispness of Emily Blunt’s Mary Poppins. The notion raises a smile, but Wintour has a politician’s sleight of hand when it comes to answering questions she doesn’t like, segueing to her preferred talking points. She steers the conversation away from her own image and on to how Vogue is championing women in political leadership. “I was very encouraged by our midterm results on that front. I believe women are taking control and standing up for what they believe in. We are in a moment of huge change.” She reels off an impressive list of female politicians who have appeared in the magazine recently, including Alexandria Ocasio-Cortez, Amy Klobuchar, Lauren Underwood, Kirsten Gillibrand and Kamala Harris.

For the best part of two decades, Wintour’s Vogue was closer to the White House than Vogue had ever been. Hillary Clinton became the first first lady to cover Vogue in 1998 – an honour not bestowed, even, on Jackie Kennedy – and in 2016, Vogue endorsed her presidential candidacy, the first time the magazine had ever been publicly partisan. But it is the mention of Michelle Obama that sends Wintour into raptures. “What intrigued me and the rest of the world about Mrs Obama from the beginning was her poise, her intelligence, her grace, how articulate she was, and the sense that she gave of being a true partner to her husband. She was remarkable in so many ways – and still is, look at the incredible success of her book – and I was thrilled to see how she embraced fashion in such a democratic way. She would wear leggings one day, a designer gown the next, and look comfortable in both. She wasn’t locked into one idea of how a first lady should dress. For Vogue, she was a gift.” When the Met’s Costume Institute was renamed in recognition of Wintour’s work as a fundraiser and cheerleader, Michelle Obama cut the ribbon, saying, “I’m here because I have such respect and admiration for this woman, who I am proud to call my friend.”

Wintour: ‘Today’s audience … wants journalism to take a stand.’ Photograph: Tyler Mitchell

Since Trump’s election, Vogue has found itself in opposition, a position it has embraced with unexpected relish. The September issue included a profile on Stormy Daniels (the adult film star who had a hush money deal with the president) which saw Daniels resplendent in evening gown and Tiffany diamonds, photographed by Annie Leibovitz. “Today’s audience – not just Vogue’s audience, every audience – wants journalism to take a stand,” Wintour says. “People want to know what you believe in and what you stand for. In this time of fake news, when there is so much disregard for truth and value and for supporting those less fortunate than oneself, we have a moral obligation to stand up for what’s right.”

While Michelle Obama starred on three Vogue covers as first lady, Melania Trump is still waiting for Wintour to call. Will Melania be in Vogue, I ask? “Melania has been on the cover of Vogue,” Wintour fires back without missing a beat. Indeed she has, in her wedding dress, in 2005, but not as first lady, representing the White House. “We do report on Melania consistently, on vogue.com,” says Wintour. “Which is Vogue.” Her inflection puts the emphasis firmly on the full stop.

‘Tennis-mad’ … Wintour at the Australian Open men’s semifinals in January. Photograph: Julian Smith/EPA

She picks up her mobile phone. “I’m going to ask someone to bring me another coffee. Would you like one?” I say no, and wait for her to make her call, but after a few seconds she raises an amused eyebrow at me. “Go ahead. I can type and think at the same time, you know.” She has texted the coffee request, I realise. As perfect as Wintour’s manners are, I do not get the impression it would be wise to put them to the test by boring her. I try not to think about the scene in the 2009 Vogue documentary The September Issue when Stefano Pilati, then designer of Yves Saint Laurent, withers under her stony-faced appraisal of his latest collection.

Born in London in 1949 to a British father (Evening Standard editor Charles Wintour) and an American mother, Wintour moved to New York in her 20s. She returned to London in 1985 to edit British Vogue, but was back in New York two years later. Her first issue as editor of American Vogue, in November 1988, featured a model wearing jeans, which famously caused the printers to call Vogue’s office to check they had the right picture. It was an early signpost of the shift from fashion being “something that was directed at a small group, to becoming something that speaks to everyone. That has been the most extraordinary change that I have seen.” As fashion has swelled to a powerful force in culture over the last three decades, Vogue has ridden the crest of that wave. A Vogue cover has become an official stamp not just of beauty, but of relevance. For Amal Clooney, Serena Williams and others, a Vogue cover has signalled a change in gear from success in their field to general superstardom. “Vogue stands for quality,” Wintour says. “To be recognised by Vogue always has an impact.”

Michelle Obama cutting the ribbon of the Met’s costume department, renamed the Anna Wintour Costume Institute in 2014. Photograph: John Aquino/Penske Media/Rex/Shutterstock

In 1998, Renée Zellweger became the first non-model to cover an all-important September issue of Vogue (traditionally the biggest of the year). As the era of the supermodel waned, Wintour coached and coaxed a new generation of actresses to take their place. “The supermodels led us to celebrity,” Wintour says. “The generation of models who came after the supers just wanted to be models, and didn’t want that spotlight. Meanwhile, celebrities were starting to engage with fashion, realising the power of fashion to build their personality, to express who they were, on the red carpet or the front row. So the supermodels ended up being replaced by celebrities.” The alchemy that happens when fashion meets celebrity is at its most potent at the Met Gala, over which Wintour (who has chaired the event since 1995) will once again preside on the first Monday in May.

But today Wintour, who rarely gives interviews, seems less interested in talking frocks than in establishing her place on the right side of history. “I hope I have been able to use the platform of Vogue to do a little bit of good in the world,” she says. She mentions the CFDA Fashion Fund, launched in the aftermath of 9/11 to support young American designers. “It has been wonderful to see Condé Nast and Vogue taking leadership in championing diversity. As a company, we want to stand for positive change. I personally take that very seriously, but it’s not just about me. Edward Enninful was such an important appointment at British Vogue, and he is leading the way on diversity.” I ask who her mentors and allies have been, and she namechecks Condé Nast luminaries Si Newhouse and Alexander Liberman, and designers Karl Lagerfeld, Calvin Klein and Ralph Lauren, before landing on Kay Graham, publisher of the Washington Post during the Watergate era. “She was a great friend of my father’s and became a great friend of mine. I admired everything she stood for, how she represented the progress of women, how she stood her ground against the White House. She believed in her editors, she had wonderful women friends and was a deeply good person and had a lot of fun. And [she] was a great tennis player.”

It is a year since the New York Times published allegations of sexual misconduct against Mario Testino and Bruce Weber, two star photographers of Wintour’s Vogue. Wintour has faced criticism for having failed to use her power to better protect the vulnerable in fashion. “We take very seriously events that happen in the industry, whether in or out of our control,” she says today, “and after so many unfortunate incidents came to light, we took a strong stand.” Testino and Weber were banished from Vogue. A new Condé Nast code of conduct forbids the hiring of models under 18, and requires images involving nudity, swimwear, lingerie or suggestive poses to be approved in advance by the subject.

Anna Wintour with her children at a Sean John fashion show in New York, 2003. Photograph: Matt Baron/BEI/Rex/Shutterstock

How long Wintour will remain at Vogue is impossible to predict, because Condé Nast is itself in turmoil. Having lost an estimated $250m over the past two years, the company recently announced plans to merge US and international operations, and is searching for a new CEO to replace the departing Bob Sauerberg. Wintour enthuses about the digital age as “a golden era for journalism, because we have the luxury of being able to talk to more people than ever before”, but digital has undoubtedly eroded the might of Vogue. The magazine’s Instagram account has 21.5 million followers but that sounds less impressive when you note that three of the Kardashian family – Kim, Kylie and Kendall – have more than 100 million followers each.

Wintour insists that she believes print magazines will be around “for ever”. Really? “Yes, for ever. I really believe that. Print remains the jewel in the crown.” Does she think of Vogue as a magazine, these days, or is it now a brand? “I don’t care for the word brand, to be honest,” she says. “It makes me feel like I’m in a supermarket. But I love Vogue – very deeply.” She types a few words on her phone and the door opens to signal our time is up. She walks me to her door, shakes my hand, bids me a warm goodbye and turns to her assistant. “I asked for a coffee,” she says. There is no discernible hint in her tone that this is a sackable offence. But then, Anna Wintour doesn’t give much away.