September 1995, past midnight in an unlicensed downtown Los Angeles coffeehouse. The door is sealed with heavy wrought-iron work, and its front steps have recently played host to a drive-by shooting. The staff can’t recommend anywhere in the area safe enough to find a real drink, and the crowd affects a studied, West Coast indifference as the Dirty Three take the stage, puffy, crumpled and ragged. They’ve played more than 200 shows since March, leaving their native Australia on a proposed three-week jaunt that has somehow stretched to 10 months, as they drive coast to coast in a 1960s Dodge Polara.

There’s no vocalist and no bass player, just a guitarist of sorts, a drummer playing as though he’s just stepped out of some loose jazz combo, and a gypsy-curled, hunched figure scraping and plucking a violin, lurching from folksy reels to squalls of ear-splitting feedback. Baseball-capped Californians are turning from the video games, jerking thumbs stageward, saying: “Hey, these guys have got something.” It’s like a scene from a bad teen rock movie, the traditional fresh-faced aspirants supplanted by a desperate, road-worn threesome who haven’t seen fresh shirts since early spring. “Now that was a great show,” recalls the group’s violinist and spokesman, Warren Ellis.

In 1989, Ellis returned to Melbourne from four years of busking round Europe and found himself at a loose end. “Australia seemed so cold after Europe that I didn’t want to do anything,” he explains. “I just went and lived out in the country and didn’t pick up the violin for three years.” Then in 1992, a friend opened a hotel and asked Ellis to play in the bar. Mick Turner, late of the 1980s band the Moodists, was recruited on guitar; drummer Jim White joined from the unlikely-named People With Chairs Up Their Noses, where he had played percussion on an ironing board covered with letter boxes and other domestic detritus. The Dirty Three was formed.

Last year, the casually tossed together trio provided a live accompaniment for Carl Dreyer’s silent classic, The Passion of Joan of Arc, at the National Film Theatre; in February, Ellis is to travel to Vienna to score a new play with countryman Nick Cave; and the band’s third album, Horse Stories, was released by Big Cat last week.

Turner is a generous and modest foil for Ellis’s amplified flights of distorted fiddle fancy, and there’s still a residue of White’s disrespect for drumming conventions in his approach. He doesn’t treat the kit so much as a rhythm source as a vehicle for sympathetic embellishment of the ebb and flow of Ellis’s and Turner’s unpredictable leads, as close to free improvisation as they are to any received notion of folk or blues. “Jim has a remarkable style,” says Ellis. “He plays very melodically. In the Dirty Three, everyone is important.”

The band’s egalitarian principles reach beyond a simple division of the limelight. Their first two albums were self-financed, and they own the rights to Horse Stories, a nine-track collection of insidious, elliptical and utterly distinctive instrumentals, and the first they’ve recorded with any certainty of a release. Ellis takes satisfaction in distancing himself from a host of smiling music execs suddenly “coming out of the woodwork”. “I was opposed to going with anyone who hadn’t been with us since the early days,” he says. “It was good to be able to put the finger up at them. It’s a pipe dream that’s come true.”

Industry manipulators could no doubt see the potential in the Dirty Three. You could plaster their album sleeves with sepia tints of cracked Death Valley sandscapes, like hints for a directed reading of their parched electric-organic explorations, and perhaps see them nudge the mainstream, but Ellis won’t have any of it. “People say our music sounds like the desert,” he says, “but I’ve never even been there. Australia is far enough away from everything for us to be influenced by the rest of the world but still have our own character.”

The closest the band come to putting a helpful gloss on their monastic purity is Ellis’s on-stage patter, which illuminates the exacerbating circumstances behind each piece in vivid purple-prose descriptions of wasted days, lost loves and drunken despair, veering from comic monologue to impassioned beat poetic. But no matter how near to high art he and his cohorts might soar, Ellis in person will always remain firmly and gloriously earthbound. It’s impossible to be pretentious in an Australian accent.

The Dirty Three are currently in America collaborating on a new record with Palace’s Will Oldham. “Where are you calling from?” I asked Ellis. “F***ed if I know…” was his reply