I've been trying to get an appointment with Valerie Vargas, one of London's best-known tattooists. I'm told that she's not taking any new customers. I've been scouring her Twitter feed on a near hourly basis for the slightest whiff of a cancellation but, so far, my attempts have met with failure.

I also try Claudia de Sabe, Nikole Lowe and Saira Hunjan, but their waiting lists are so long that, by the time they bestow their colourful gifts on my skin, men might be able to give birth. "Female tattooists are definitely more sought after now than when I started tattooing 16 years ago," Hunjan tells me. "When I was 14, I rang every tattooist in the yellow pages looking for work experience. They seemed shocked to hear a girl's voice, and, tellingly, only one agreed – after he'd spoken to my mum and explained there would be 'lots of swearing'."

Hunjan explains that the London Tattoo Convention, now in its eighth year, was instrumental in forming a network of female artists. When I visited the 2012 event last month and walked around east London's Tobacco Dock, enveloped in the acerbic buzz of tattoo machines, it was evident that not only are tattoos big business - the convention figures increase year on year - but that all eyes are on the female artists such as Lina Stigsson and Angelique Houtkamp, who have a constant swarm around their shared booth.

"There's been a huge increase in the number of female artists in the past five years," Stigsson tells me. "It's a hugely progressive industry in terms of gender equality."

The number of tattoo parlours in Britain has almost doubled in the past decade, and in that time both genders have been attracted to what can be a lucrative profession. And with 20 million of the 62.6 million of us in the UK inking our bodies, the aesthetic of beauty is shifting. When talk turns to tattooed celebrities such as Angelina Jolie or Rihanna, everyone agrees that they have helped the business: "People think, 'If she can get one, I can too.' They make tattoos real," Houtkamp says.

Women are increasingly attracted to the world of tattoos … the International Tattoo Convention in 2011. Photograph: Martin Godwin for the Guardian

TV has also played its part. Programmes such as Miami Ink and its LA, NY and London spin-offs offer a snapshot into the tattooing world, and women feature heavily, both as artists and customers. The LA Ink protagonist Kat Von D has combined her tattoo talent with sharp business acumen, expanding her offering to clothing and makeup lines. "Kat's a household name in the US, but a credible artist too, and that, more than anything, is empowering for female artists," says Hunjan, who has herself collaborated with the luxury English leather brand Ettinger.

Houtkamp thinks that the art itself could be why female tattooists are more in demand. "I think women are more attracted to what female artists draw and might feel more comfortable with a woman tattooing them," she says.

The UK's second annual Female Tattoo Artist show takes place on Sunday, with upwards of 50 artists displaying their work. It is in its infancy, but Stigsson isn't convinced a women-only show is a positive move: "Female tattooists are doing so well now that we really don't need any special treatment." I might still go, however. After all, I need to find the next Valerie Vargas.

• The Female Tattoo Artist show takes place on 7 October 2012 in Leamington Spa.