Written on the body: Tattooists at pains to point out their artistic credentials

Welcome to the modern art museum, where hundreds of illustrators, graffiti taggers and fine artists offer up their services – with only one rule: you must take their work home on your skin.

Thousands of people visiting the Great British Tattoo Show this weekend in Alexandra Palace, north London, are happy to oblige. Around 250 tattooists from all over the world fill the bustling exhibition space; it is thought they will take home more than £350,000 in two days. But please don't ask them for skulls, British bulldogs, or dolphin tattoos. They are here, each one insists, to sell art.

Around one in five Britons is inked, and the recession-proof industry is growing. Cara Delevingne, a model, has just got giant script-like initials tattooed on her hand, one week after she got a lion tattoo on her index finger. Hardly a day goes by without One Direction heart-throb Harry Styles showing off his latest tattoo, and even the singer-songwriter Ed Sheeran boasts an arm covered in artwork. And that's before you mention David Beckham or Peaches Geldof. Top artists can expect to earn around £50,000 a year.

"In the last 12 to 18 months, there has been a real stride in tattoos being accepted as art," said Sion Smith, editor of Skin Deep, the UK's best-selling tattoo magazine. "There are artists operating out of private studios, in churches, without any advertising – who don't even want to be known. We're seeing buyers travel to Japan for full-body dragon 'suits'. More artists are coming out of Eastern Europe, and more and more women are getting tattoos."

Laura Lenihan, 25, an apprentice from Purley, London, agrees. The fine-art student and London College of Fashion graduate says: "I wanted to be a tattoo artist from when I was 14. But my parents didn't want me to do it. They associated tattoos with outcasts and bikers. But now it has blown up so much. I can show them the kind of work that can be done and that I can make a living."

Jade Tomlinson, 27, graduated from Norwich School of Art and Design and now splits her time between London and France, where she and her colleague, Kev, create paintings, drawings and sculptures. They have been designing tattoos for two years. "We're illustrators first and foremost, but our discipline sort of evolved into tattooing," she said. Ieva Birzina, 22, an advertising management student from Latvia, has travelled the world in her two-year search for the perfect tattoo artist. She says she prefers some of the body art she has seen to a lot of "modern art pieces [I end up] seeing in museums".

Traditionalists do not seem to mind the change. Mark the Shark, 44, a tattoo artist from Liverpool, has been working for more than two decades. He says the "industry needed to change. It was dying a death until a whole new group of people came along. We needed to embrace it."

And it is not exclusive to the underground. Jeremy Waddington, 38, a banker, has seven tattoos, including one on his neck. "You never know what people have under their clothes," he says.