In terms of unlikely events, the appearance of a band whose back catalogue includes the evocatively named albums Urine Palace, and Spit Bucket in the music programme of the Edinburgh International Festival, surely ranks high. But The Tiger Lillies, who on Saturday mount their Tribute (of sorts) to Monteverdi in the Usher Hall, are not surprised at all. "We're the band of choice for highbrow festivals looking to round out their portfolio with a naughty night. They actually want us to offend people," sniggers Martyn Jacques, "criminal castrato" and accordion-playing lead singer of the group, whose cult following stretches from Mexico City to St Petersburg.

This, says Jacques, when we meet in a cafe in London's Gloucester Road tube station, is his first experience of Monteverdi, despite a succession of classical projects: last year they played a Mozart concert in Vienna as part of the official 250th celebrations.

When EIF Director Jonathan Mills sent him a CD of Monteverdi's Madrigals of Love and War, his reaction was not encouraging. "I thought Monteverdi was an alien. I couldn't understand what he was saying 400 years ago he was meant to be subversive, but it didn't seem very subversive to me.

"I couldn't recreate the music, so I concentrated on the text instead. I'm pretty pleased with the result. I don't really believe in ghosts, but I do think there is an essence of Monteverdi."

What The Tiger Lillies have come up with - Songs of Love and War - is, on the evidence of the preview CD, both aural seduction and assault in the same breath. There is edgy beauty, rage and a sense of politics. "I could say straight up that the world is going to pot and capitalism isn't working, but sincerity is dull, isn't it? That's where irony comes in. Basically, while more commercial artists are out there saving the rainforests and feeding the world, we're in some bar that smells of p*** playing to a bunch of alcoholics." It sounds a lot like seventeenth-century Venice, as Monteverdi fanatics might note.

It's not easy to describe The Tiger Lillies, a three-man outfit who are best known for their brilliant "junk opera" Shockheaded Peter which toured worldwide in the 1990s, but if you took the spirit of the lascivious, fornicating grotesques on the edges of medieval manuscripts and shoved it into an underground cabaret club reeking of booze, fags (remember that?) and sex, then added an accordion and transposed the whole thing up two octaves to a maniacal falsetto, you might come close. Critics talk about Kurt Weill and 1930s Berlin; The Tiger Lillies call it "satanic folk", but that's simply to avoid just such convoluted answers to the question: "So what sort of music do you play, then?"

They are famous in Russia ("our records are in all the shops, but they're pirate, so we never make any money") and "enormous in Greece" (where they recently played a 1200-seat venue to sell-out audiences, despite Jacques spitting on the front row every night - "well, they would insist on talking through the gig"): Usher Hall row A take note. They have played for everyone from the Rothschilds to neo-Nazis, from the peak of an Austrian mountain to a platform above a kitchen in a backwater Mexican restaurant. The more sedate audiences of the Usher Hall do not worry them, because what The Tiger Lillies really want is mainstream success.

"I dream of business class!" says long-haired Jacques, a little unfeasibly, protesting about flogging CDs after their concerts "like barrow boys". It's a thin complaint: he loves hamming it up almost as much as he likes spinning a line. "I don't want to be cultish. Perhaps a mogul might read this article and take pity. I want people to buy my records and make me rich, but it's ridiculous. We should rename ourselves Commercial Suicide. Everything we do takes the p***. You have three choices as an artist as you get older: you die, you disappear into poverty and obscurity, or you become mainstream. The problem is, I made a big career mistake. I really should have taken heroin or something. You've got to be tragic if you want to be a legend."

Jacques, with what might traditionally be termed his "colourful" past, has all the trappings of cult legend, from when he first picked up an accordion while living above a brothel in Soho, to the suggestion that The Tiger Lillies were Marilyn Manson's ideal wedding band. The band's existence can be traced back to Jacques's failure of the 11+ exam. "Instead of going to grammar school with my friends, I went to a really rough state school in Slough, a cauldron of racial tension and knife fights. I developed an enormous sense of alienation, like most weird people. If you feel at one with the world and content in it, you probably don't write about buggering hamsters."

Jacques assures me that, contrary to their image as subversive, anarchic and rude, the band enjoy the quiet life - not just to placate an Usher Hall audience that may consist entirely of old ladies. "Some of our best fans, actually we have a fan in Russia, a famous singer who's covered our tunes, who insists on trying to take us to brothels every time we go there. It's terrifying. We're a bunch of wimps and nerds really. It's not quite early to bed and a nice cup of cocoa, but it's not far off."

Will he ever tire of bawdy inspiration, of urine and prostitutes? "What else is there but urine and prostitutes? That's a good title actually, I'll call our next album that. When I started out 20 years ago, I was only mildly offensive, but then you realise people want you to be more disgusting, so it becomes a challenge. The problem is, it's humour, it's ironic. I've never stuck a hamster up my a***, no matter what the lyrics say. But some people don't actually seem to understand that."

  • The Tiger Lillies: A Tribute (of sorts) to Monteverdi; Usher Hall, Saturday, 8pm.