It is Memorial Day weekend in America, the unofficial start of summer, and my friend and her teenage daughter are in the Hamptons, having scored an invitation to stay at the beachside mansion of one of New York’s wealthiest families.

“What are you going to wear?” I asked my friend, before she set off, mindful of the grey and drizzly weather and the fact that grand-style entertaining isn’t her usual milieu. “Oh, I’m not worried,” she replied breezily. “We went to J Crew.”

A mother and daughter both buying clothes from the same retailer could be rather odd, but J Crew is a revered American fashion brand that manages to cater to the tastes of different generations. The clothes are affordable and stylish and wildly popular in the US. Last week, British shoppers got the chance to buy a limited J Crew collection at a pop-up shop in London’s King’s Cross, before the American retailer’s high-profile and much-flagged first British shop opens in London’s Regent Street in November.

Overseeing this foray into Britain is J Crew’s president and creative director, Jenna Lyons, widely credited with transforming the company from a fashion retailer that had lost its way into a cult brand. The company has more than 300 branches in the US, a growing presence abroad and revenue of more than $2.2bn (Dh8 billion). The 44-year-old is currently the most high-profile woman in consumer fashion. This year, she was ranked in Time magazine’s 100 Most Influential People list.

Lyons has been with the brand for her entire career, having joined as a junior designer in 1990. When former Gap CEO Mickey Drexler took the reins of the struggling brand a decade ago, Lyons said that both she and the company were burned out by a corporate strategy that had lost interest in creativity and was simply trying to hold on to the bottom line. “We were lost soldiers, working away, following orders,” she remembers of the era when J Crew lost its mojo. “I was shell-shocked fried.”

On Drexler’s second day in the job, he asked Lyons what she thought of the clothes and she decided to be completely candid because she felt it was a do-or-die moment for the business. Of three pairs of women’s trousers on offer, she told her new boss that only one was right for the brand. They went through the entire women’s collection, with Drexler ordering her to throw disliked garments on the floor. She said she hated a boucle sweater that reminded her of poodle fur. She wasn’t keen on most of the T-shirts. She thought they had compromised on the quality of cashmere. They didn’t have any decent jackets. And so it continued.

At the end of the session, there were piles of discarded clothes on the floor and a capsule collection of “brand-right” clothes left on hangers. Drexler told her to go off and fill in the gaps. Given free rein, Lyons brought in new styles that reflected her quirky and androgynous fashion taste. She made things more interesting by doing collaborations with high fashion designers such as Prabal Gurung and traditional American shoe brands such as Sperry Topsider. To this day, if you want classic boat shoes in gold and silver, you can only find them at J Crew. Many Americans who had grown up with the brand – it started out as a catalogue-only company – watched it being transformed before their eyes. Soon, customers came back. The brand was given a boost when Michelle Obama and both of her daughters wore J Crew in public.

Lyons also embarked on a bold overhaul of the brand. She felt the different arms of the company, from retail to catalogue and online sales, were fractured and working against each other. She redesigned the shops, putting in expensive fittings and giving them a more fun and classy atmosphere, and she helped shape a stylish marketing strategy that enlisted the talents of fashion photographers and fashion bloggers.

She herself featured in many of the company’s catalogues and in 2011 – by this time she had been made president and chief creative director – there was the famous incident that was dubbed Toemageddon by the Daily Show host Jon Stewart. In a photo-essay for the company’s spring collection catalogue entitled My Weekend Lyons was featured at her townhouse in Brooklyn painting her then four-year-old son Beckett’s toenails with neon pink varnish. It sparked a debate about gender identity that left America’s social conservatives fuming and liberals thinking it was no big deal. Then came the news that Lyons’s nine-year marriage to artist Vincent Mazeau was over and she had started a new relationship with a woman, jewellery designer Courtney Crangi.

In what must have been an uncomfortable few months, Lyons was the subject of feverish gossip. Even the sale of the couple’s marital home for $5m became a big story. It had featured in Elle Decor and was suitably fabulous. Pictures showed that Lyons had her own dressing room, complete with fireplace.

She moved to Tribeca in downtown Manhattan, weathered the gossip and continued to make J Crew into a fashion force to be reckoned with. Her unusual looks – she is over 6ft tall, wears huge glasses and dresses, of course, in J Crew – means she is photographed regularly. She is well-liked within the notoriously bitchy fashion world and has, rather surprisingly, become a role model for young American girls. This may be because she has always thought of herself as an ugly duckling. She was born with incontinentia pigmenti, a genetic disorder that led to periods of baldness, scarred skin and teeth problems. She is open about the fact that she has dentures. She has confessed that as a child growing up in California she was bullied.

“It’s amazing how cruel kids can be and superjudgmental and just downright mean,” she recalled in an interview. Her interest in fashion came after her grandmother bought her a subscription to Vogue and she was captivated: “I felt a huge drive to make clothes that everybody could have because I felt ostracised by that world of beauty and fashion.”

She is having the last laugh now, with a salary rumoured to be at least $5m a year and a loyal fanbase of women who admire her and the clothes she and her team design. Martha McCarthy and Jocelyn Dorszynski are both 24 and run thejcrgirls.com, a blog focused on J Crew fashion.

“There’s an aura about her,” McCarthy says of Lyons. “She’s so unusual-looking and honest about her life and she makes clothes we love to wear. I couldn’t care less about her personal life. We like her because she’s a talented, stylish person.”

The young women have grown up with J Crew and say it has even crossed over into the American vernacular. “When we’re on Twitter, we’ll say we’re currently crewing a Jackie O type sweater as a way of describing what we’re wearing or we’ll say we’re going crewing on a Saturday morning as a way of saying that we’re going shopping.”

It’s a fair bet that other fashion retailers have tried to poach Lyons, but she seems happy with her lot at J Crew and fiercely faithful to her boss. According to insiders, she and Drexler share the same enthusiasm and energy for work and make a good team. He is known for his considerable ego and for being abrasive and effusive, while she is self-deprecating and knows how to get the best out of people.

Other high-powered women in fashion might want to start their own label but fashion insiders say Lyons is happy having free rein at J Crew and is grateful that Drexler lets her do what she thinks is right.

It is by no means certain that the J Crew style will make a successful leap across the Atlantic. What looks good in one country can seem out of place in another and many American brands have failed to connect with British sensibilities. Certainly, British fashionistas are excited about the arrival of such an essential American brand, but it’s not yet clear if Lyons’s preppy-with-an-edge range of shift dresses, capri pants, cashmere cardies and chunky necklaces will find favour with down-to-earth British shoppers. If I had to place a bet on it, however, I’d say the answer will be a yes to J Crew.