A blue and red flowering, sinuous, inky design written permanently into the skin of bare legs may be eye-catching – but is it art? Amy Savage thinks so. She explains how she got the tattoos on the backs of her legs from Xam, a noted tattoo artist who works at London's Exmouth Market. She and companion Eddie Boxell, who has equally rich and beautiful tattoos covering most of his left arm, "collect" their tattoos from noted practitioners: "It's an art thing, a collecting thing," says Boxell.

They are early arrivals among the 20,000 or more visitors expected to attend this weekend's International London Tattoo Convention at Tobacco Dock in Wapping. The expansive halls of this converted warehouse have become a fantasy realm of tattoo parlours, tattoo museums and supply stores, with alternative fashion boutiques, a rockabilly club and performance stages to entertain the decorated multitudes when they tire of photographing and praising one another's illuminated flesh.

It is a skin thing, you notice, as more and more people with ever-more impressive markings flow into Tobacco Dock. You find yourself ignoring clothes and looking at an inky foot, a spider-web neck, a dragon shoulder. The decorations shine up skin, make it different and mysterious. They lead your eyes and hold your gaze. A Japanese geisha portrayed on someone's arm; a woman going by with elegant tattoos all over her arms and on her legs, under her tights.

"People who are into tattoos know that it's an art," emphasises Savage. She is a tattooist herself, and is here to shop for equipment as well as survey the scene. She and Boxell both got their first tattoos when they were below the legal age of 18. They were 16 and 14 respectively, so they have a lifelong love affair with emblazonment. But what they both admit began as "rebellion" has matured into aesthetic wonder and appreciation.

They are participants in a cultural wave as huge as the Pacific surf, the islands from which the word "tattoo" originated. Chiara and Fabio are part of the same movement or fashion or compulsion: they have come from Italy especially for the convention, parading faces completely covered in phantasmagoric designs finished off with piercings. At its extreme, tattooing might seem a radical subculture that defines your whole existence, but the growing popularity of tattooing belies any such assumption.

Chances are that you, a family member or a friend has tattoos. Once associated with sailors, gang members, or circus performers, these markings are now a mainstream cultural force. If you don't have tattoos close to home, you surely see plenty of people around who sport the kinds of spectacular, high-quality inkings that are walking around this convention floor. Sally Feldt, editor of Total Tattoo magazine, has seen the change happen. She got her first tattoo 30 years ago and has had a ringside seat at the cultural explosion. "It's definitely more socially acceptable, more creative. It encompasses every age now, every walk of life." It is not only young people who are taking the plunge, she stresses: "I know people in their 60s getting their first tattoo."

Feldt admits there are no official figures on the growth or scale of tattooing. "Guesstimates vary: between 20 to 30% of the adult British population now have a tattoo." That figure takes it well outside the limits of a subculture and into the mainstream. One proof of this success is her glossy magazine that sells in Smiths and at supermarkets. In the past five years the magazine has gone on sale at Morrisons and Asda, evidence that a once-rarefied passion is approaching the norm.

But again – is it art, as visitors to the London convention claim?

The answer is a flaming dragon of a yes. Not only is this an art, it is one of humanity's most ancient arts. The once-salty docksides of Wapping provide a historically resonant place to stage this festival, for it was sailors who were known for their tattoos in the 18th and 19th centuries. The European "discovery" of tattooing dates from Captain Cook's exploration of the Pacific in the 18th century. Cook took artists and scientists on his voyages, and on the islands in the Pacific they encountered peoples for whom it was habitual and ritualistically important to decorate the body using a bone needle to force natural dye deep into the skin.

Modern tattooing, which is being done all around me at the convention by parlours offering state-of-the-art markings, is just a more hygienic (hopefully) and technological version of this ancient method. Tattooing flourished in the inhabited Pacific islands, yet each practised a different style: Maoris combined tattooing with facial scarification, Marquesas islanders wore full-body tattoos, Samoans preferred them on buttocks and thighs. The word for this art was "tatau".

For the first European visitors, these islands, above all Tahiti, seemed paradisiacal dreamlands of free love and unashamed physical beauty. In 1789 the crew of the Royal Navy ship HMS Bounty, seduced by the alternative society they saw among the islanders of the south seas, mutinied against the formidable Captain Bligh. As an expression of their radical choice to stay in the Pacific and reject their Britishness, they got tattoos. Since then, tattooing has become a nautical stereotype, then the stuff of 1950s fairground subculture, and now a mainstream body art celebrated in picture books and conventions.

In fact, the historical curiosity of today's tattoo enthusiasts leads them to look far earlier than the Pacific encounters of Cook and Bligh. At the convention, Japanese tattooing is on offer – the origins of tattooing in Japan go back into prehistory. At a tattoo museum tucked in among the stalls, it is stressed that some form of tattooing is universal among ancient peoples, including the blue woad-covered Britons described by ancient Roman historians. It was also customary in Rome to tattoo slaves.

Is the rise of tattoo, then, a return to our roots, a modern tribalism? The trouble with such catch-all theories is the self-consciousness of tattoo enthusiasts about their art. There are "tribal" tattooists here, but that is just one genre. Savage, for instance, says she tattoos in a "neo-traditional" style, specialising in figures such as Gypsies that she renders in a convincing, precise manner.

Entranced as I am by the strange beauty of blue, green and red limbs in the sun that filters through the Tobacco Dock skylights, I cannot imagine getting a tattoo myself. Perhaps understanding my own resistance is a way to understand other peoples' acceptance. My first boundary is the obvious one.

"It all relatively hurts," says Savage, "but some hurt more than others."

So, there's the pain. And the more extensive, rich, careful and beautiful the work of art that is pounded by a needle into your body, the longer you have to endure that pain. That makes tattooing a rite of passage: and so it was among the Polynesians before Christian missionaries discouraged them from marking their flesh. Getting a ritual tattoo in the pre-modern Pacific was a way of becoming a man, a warrior, a chief. It was considered erotic, bu paradoxically repelled the god who ruled Paradise. Before he could be buried, a tattooed chief in the Marquesas had to have his skin removed postmortem to be allowed in heaven.

It is the weight of ritual, the sense of undergoing something that changes you, that stops me personally from ever considering a tattoo. But it must also be part of its attraction. Just by visiting a tattooist such as the celebrated Danish artist Eckel you can change who you are. The change is permanent. You are a work of art.

In the Pacific, anthropologists have associated tattoos with a fragmented conception of identity, a belief that a person is not one but many things. Putting on the shining painted skin of a warrior changes your nature.

Are people now seeking to change their natures, to become fabulous new beings? Perhaps there is something digital and post-human about it all, a new sense of self that is no longer bounded by being inside your own skin, but penetrated – as by a needle – by social media and constant internet information, so you feel part of a larger entity, that imprints itself on your body.

Well ... that's as maybe. What I actually feel at the London Tattoo Convention is a seductive sense of adventure, exoticism and fun. It has the feeling of a fantasy world, an escape from workaday reality. Rockabilly is playing, people are parading their opulent chromatic skins, and to be honest, if I stayed here much longer, I might start to get tempted by those parlours after all. The modern art of tattoo is beguiling, magical and sexy. Why would people not be lured into its fantastic alternative universe, where spider webs sprout on backs and flowers on elbows?

Outside is the economic news. As the world gets tougher, the appeal of some kind of escapism grows. Like getting a 1940s hairstyle (also popular here) or reading fantasy stories, being tattooed is a way of breaking out. It's just a bit more permanent and dramatic, and therefore more intense and efficacious. "You must change your life", as the poet Rilke wrote, looking at a nude statue of Apollo.

The convention is open today and tomorrow at Tobacco Dock, 50 Porters Walk, Wapping, London