Strewth, what a sight. A busty brunette calling herself Miss Immodesty Blaize takes to the stage wearing a pair of silver nipple tassels. At first she vigorously shakes them, then she turns them in alternate directions — apparently a rare feat in this specialist area — and the audience lets out a collective gasp. "I love that moment," purrs Blaize after the show. "People who haven't seen it aren't expecting it, and the people who have are waiting with bated breath." How does she do it? "It's all in the knees and the elbows. It's like riding a bike — easy when you know how, but it can take a long time to learn in the first place."

The undisputed queen of British burlesque, Immodesty (aka Kelly Fletcher), should know. The 28-year-old revived the 19th-century art form for a British audience in 2003, when her tassels appeared in a Goldfrapp music video. Now Blaize, her co-star, Walter — a camped-up vaudeville comic — and a troupe of raunchy dancing girls are unleashing their unique style of burlesque in London's West End. The show is the brainchild of the adman Trevor Beattie — responsible for French Connection's FCUK campaign, and the Labour party's banned posters depicting Michael Howard as a pig. Beattie says: "It's sexy, intelligent, funny, camp, energetic, satirical, risquè, androgynous, exuberant, and at least seven other camiknicker-clad adjectives."

The show looks like cabaret, but with a twist. The primary attraction is the sex, but it's a sexiness that doesn't alienate people. It's erotic, not blue; suggestive rather than explicit.

"And clever and funny," adds Blaize. "Britain hasn't seen anything like this since 1860."

"Burlesque" comes from the Italian word burla, for joke: its origins lie in the British music halls of the 1840s. The term was first used to describe comic plays that entertained the lower and middle classes by poking fun at the social habits of the upper classes, an act know as "burlesquing". Combining aspects of old theatre, vaudeville and Victorian sideshows, they used satire, colloquial language and dancing girls to keep bums on seats.

In 1867, burlesque's first superstar, Miss Lydia Thompson, from London, and her troupe were exported to the United States by the impresario P T Barnum, and became an instant hit, spawning a whole industry of new starlets and troupes. Most famously, burlesque created what we now know as striptease, first performed at the Chicago World's Fair in 1893 — though the term was coined later, in the 1920s, by the New York promoters the Minsky brothers.

"At first, the striptease was just a bastardised form of belly dancing," says Blaize, who started performing as Immodesty six years ago.

"Then it grew into the dance we now know as the hoochy-cooch, which involved lots of shimmying of the bum and breasts." Later it was given an artistic twist by performers such as the American fan-dancer Sally Rand (1930s) and the former vaudevillian Gypsy Rose Lee (1930s and 40s). It wasn't just about ribald humour and scantily clad women, though: comics, singers, jugglers and magicians were also important parts of an authentic burlesque show. As time went on, however, the strippers increasingly dominated the routines. They also became more graphic and trod the fine line between titillation and propriety. To avoid total nudity, the ladies covered their groins with flimsy G-strings, and used tassels on their nipples. Gypsy Rose Lee was continually arrested for revealing too much. By the 1950s, striptease was the last surviving part of the burlesque tradition; by the 1960s, hardcore pornography had become readily available, so most burlesque shows disappeared. The best burlesque comics segued into radio, film and television: Jackie Gleason, Fanny Brice, W C Fields and Bob Hope all began their careers in burlesque. The legacy lives on, however. Every time a comedian uses a double entendre, or mimics a politician or a movie star, you are watching burlesque in action.

And then there are performers such as Miss Blaize, who has the gas man to thank for her stage name. "He appeared at my door to fix the boiler, and told me I looked like the cartoon character Modesty Blaise. I was like: 'Yeah, sure, Immodesty Blaize, more like!'" Does she think it's the sex or the comedy that attracts the audience? "It's all those things. It's glamour, it's the escapism, it's the humour, but most of all it's bloody good fun." Sometimes it's a double whammy of satire. One of Blaize's shows features a reverse strip (clothes put on, not taken off), followed by Walter doing a cowboy striptease set to punk rock. And the audience loves it. Also, a modern-day burlesque audience is expected to dress to impress, so fishnets, cleavages, walking canes and top hats are common sights at the shows, which adds to the heady atmosphere.

Amazingly, Blaize initially found it difficult to find places to perform. "People didn't understand burlesque," she explains. "Then I did the Goldfrapp video and suddenly here was this amazing nipple-tasseller on MTV and people were saying, 'Oh my God, what's that?' I'm no size-8 Kate Moss, and I guess it was a refreshing change to see someone who is an incredible performer and who isn't a stick insect. Suddenly I was doing anything from the Cannes movie festival to awards ceremonies and charity events."

The future looks bright. There is talk of a Broadway show, and increasing bookings.

"The sky's the limit, as far as I'm concerned," she says. "For a long time, people were thinking about the future, about fast cars, space travel, the internet, internet porn — and now we've had that. The new fantasy is looking back, at the good old days of the Hollywood bombshell, of the slinky starlets. You can see it in everything from interiors in bars and clubs to fashion — in corsetry and a more constructed female form. There is a huge scene in America, in New York and LA. Burlesque's influences are far-reaching, and it's here to stay if I've got anything to do with it."

Immodesty Blaize & Walter's Burlesque! opens at the Arts theatre, London WC2, on Wednesday