Dressed in killer heels, ruby-red lipstick and a velvet dress that leaves little to the imagination, the boss of healthy-living restaurant chain Leon totters to the podium. John Vincent is ready to gee up the troops.

“You guys are a f****** ecosystem,” he yells with a toothy grin. Nobody is quite sure what it means, but they cheer anyway. Seconds later, Vincent praises the accounts team for their speed and diligence.

Welcome to the surreal world of Leon, the rapidly expanding purveyor of fast food. You can’t accuse Vincent of shirking a challenge. Later this year, he will take the chain’s lean, clean green shakes and falafel hot boxes to America — land of the burger and the 60in waist.

Vincent, who appears to be sporting fake breasts beneath his frock, is Leon’s kung fu fighting chief executive. He is speaking at a company conference where the theme is “learning to fly”. The boss has come as an air hostess.

When we meet, the 45- year-old is more conventionally dressed but no less excitable. “I feel like I’ve got some giant Fisher-Price play centre and every year you get given a new bit to play with,” he says at one of Leon’s London eateries.

Vincent set up the company in 2004 with Henry Dimbleby, son of Question Time’s David, and the chef Allegra McEvedy, now a staple of TV cookery shows. After a few false starts, business is booming. Leon’s 43 restaurants, mainly in the capital and southeast England, are a rictus grin of relentless positivity and attract droves of health-conscious office workers.

For many, dishes such as chicken superclean quinoa salad and sweet potato and okra stew have replaced sandwiches and crisps as their lunchtime fare. In 2015, sales grew 48% to £37m and are expected to have risen sharply again in the past 12 months.

Despite all this, Leon has an image problem. Or at least it had one. “People used to call us the Guardian-reading lesbian brand,” Vincent says, leaning towards me as if revealing a secret. But the chain’s appeal is broadening, the boss says, as more people are turned on to healthy lifestyles.

“We’re all Guardian-reading lesbians now,” he concludes, with a guffaw.

To hasten Leon’s breakout from the metropolitan elite, Vincent has a shocking confession. “I don’t actually read The Guardian,” he whispers sheepishly. This goes to the heart of the business — and its boss. Fluffy and friendly on the outside; hard-nosed and driven on the inside.

“We don’t have cliques, we are one team,” he tells the management conference. “You are either part of that team, or you are not part of Leon.”

Vincent likes to push boundaries. At the home he shares with his wife, the broadcaster Katie Derham, he practises wing tsun, a type of kung fu mastered by Bruce Lee.

Last year, he sent baristas from Leon’s restaurants on an intensive wing tsun course. He wanted them to speed up their hands, so they could serve coffee faster. Leon is soon to open a kwoon, or martial arts academy, in Soho, central London, where its 850 workers will be able to take lessons to improve their well-being.

The wholesome food, the smiling staff, the quirky pictures of the founders and their families that hang on the walls, all make it feel as if frowning in Leon would be a crime. Vincent often visits restaurants unannounced and has a “four-minute rule”, where he will not say anything negative for the first 240 seconds.

It may sound like new-age jargon, but whatever Vincent is doing, it seems to be working.

Leon has been at the vanguard of a revolution in the way we eat food. When it started 13 years ago, the idea of a sugar tax on fizzy drinks or a ban on junk food ads during children’s television would have sounded crazy. Both are now likely to be introduced within two years.

The willingness of politicians to police what consumers eat and drink has forced some of the world’s biggest food companies to look to the British chain for inspiration. The boss of KFC in Britain has said he wants to be more like Leon. Salad, fruit and carrot sticks have started to appear on the menus in McDonald’s.

The high street has also changed dramatically since 2004. Back then, Woolworths was still trading and most towns had a Blockbuster video store. Now “the whole high street is food”, Vincent says.

The chief executive is part new-age spiritual thinker, part hard-edged capitalist. He talks about wanting to have a positive impact on the world through business, but “not in a sandal-wearing way”.

“John is charismatic and likes to come across as off-the-wall,” said a well-known City dealmaker who worked with him in Leon’s early days. “But he’s not a stand-up comedian. He’s clever, switched-on and incredibly well connected.”

Vincent is desperate to be a man of the people. His accent is tinged with mockney and he swears copiously. He loves Billy Bragg and twice tells me he went to a state primary school.

However, the everyman shtick masks a privileged upbringing. His early years in state education were followed by Haberdashers’ Aske’s, the Hertfordshire public school for boys, where he was a contemporary of the comedians Sasha Baron Cohen and Matt Lucas. In such company “you had to get by on banter”, he says.

After school came a first-class history degree from Cambridge. In between studying, he organised rave parties with Richard Reed, co-founder of Innocent Smoothies. College was followed by stints at the consumer giant Procter & Gamble and the American management consultant Bain. He met Dimbleby at the latter — the pair spent their lunchtimes “plotting our escape”.

It is hardly a rags-to-riches tale, yet Vincent genuinely does things differently — a practice that goes beyond dressing up as an air hostess.

Indeed, his ambitions are far loftier than merely increasing restaurant sales. His goal is for kale and peanut salad to become the new burger and fries. “We want to be as ubiquitous as Coca-Cola, as ubiquitous as iPhones,” he says. “That’s what we need to be to become the new fast food.”

Selling £6 salads to City slickers is one thing. Convincing those on lower incomes to buy Leon’s “naturally fast food” is a different proposition.

Vincent admits it is still “too much of a middle-class brand”. Almost all the restaurants outside London are in affluent enclaves, such as Brighton, Oxford and Cambridge. There are plans to open in Manchester by the end of the year and there is an outlet at Birmingham New Street station, hardly deprived areas.

When will Leon open in Sunderland, or Plymouth, or any city struggling with unemployment? Vincent says he will open “in an area that isn’t wealthy” by the end of next year. The lower rents will allow him to reduce menu prices, but the range of food on offer will not change, he adds.

“You don’t dumb down. You don’t compromise. iPhones exist in the middle of poorest areas. Apple didn’t do that by trying to become mass [mar–ket]. The mass came to them.”

Before Sunderland, Leon is going to Washington DC. The company will decide on a location in the next two weeks and intends to open by the autumn. It is following in the footsteps of the sandwich chain Pret A Manger, which has sites in several American cities.

Funding for Leon’s early US expansion is most likely to come from “the existing balance sheet”, Vincent says. Investors include the private equity firm Active as well as Vincent and Dimbleby family members. The TV personality Alexander Armstrong and sports presenter Gabby Logan are also shareholders.

If Washington is a success further American locations will be considered, as will external investment. “I expect in 18 months we’ll still have only three restaurants in America, but then we’ll really put the foot on the gas.”

For now, Leon has more pressing concerns at home. Rising business rates, food price inflation and Brexit- related economic uncertainty could make this year bleak for many restaurant chains. “This government is doing nothing but screwing up our industry.”

Among Vincent’s biggest worries is freedom of movement after Britain leaves the EU. Leon has seen a 20% drop in job applications from workers from the Continent since the vote. He made a film for staff explaining that they were not being rejected as individuals. “It became a real morale issue,” he says.

“We can’t just have nuclear physicists let in, we’ve got to have people who can do this,” he says, pointing at the kitchen. Food company bosses may have their concerns ignored because they are not invited to “the dinners between the bankers, the car makers, the politicians”.

Whether ministers can negotiate a Brexit deal to satisfy Vincent remains to be seen. They would be wise not to pick a fight with him, though. He knows his kung fu.

The life of John Vincent

Vital statistics

Born: December 28, 1971
Status: married, with two children.
School: Haberdashers’ Aske’s, Hertfordshire
University: read history at St John’s College, Cambridge
First job: court reporting assistant
Pay: £150,000
Home: Haywards Heath, West Sussex
Car: Audi A4
Favourite film: True Romance, starring Christian Slater and Patricia Arquette
Book: The Great Work of Your Life: A Guide for the Journey to Your True Calling, by Stephen Cope
Music: Billy Bragg
Gadget: knife sharpener
Last holiday: Brazil
Charity: Greenpeace

Working day
The chief executive of Leon wakes up any time between 5am and 7.30am. Every other day, he does the school run with his daughters — Natasha, 16, and Eleanor, 11. Vincent visits at least one of Leon’s 43 restaurants every day, often without warning staff. The goal, he says, is to “catch them doing stuff right”. The rest of the day is spent at Leon’s headquarters in Borough, near London Bridge, or visiting sites for new restaurants. Vincent has had a “big issue with lack of sleep” and now bans himself from working after 9pm. He has disabled email on his phone.

Downtime
As well as practising wing tsun, a form of kung fu, Vincent loves to sail with his family. They own a Beneteau yacht. Last summer, while visiting the Greek island of Kefalonia, they sailed past Lionheart, Sir Philip Green’s superyacht.