Stephen Page, the artistic director of Bangarra Dance Theatre, is disarmingly honest. Invited in 1997 by the Australian Ballet to choreograph a version of The Rite of Spring that would unite classically trained dancers with members of his own Aboriginal troupe, he confesses to an unusual initial reaction to Stravinsky’s clamorous score. “I knew Stravinsky’s name,” Page says, “but I wasn’t familiar with his work. So, in the innocence of my ignorance of Western classical music, I listened to Rite a couple of times at night and it was so exhausting that I fell asleep!”

He can laugh about it now, but at the time Page was understandably nervous. “I was scared. People were saying to me, ‘You’re tackling Rite of Spring? Oh no, don’t! Every choreographer tries and never succeeds.’ ” Eventually I thought, OK, just relax and surrender to it. In the end I tried to draw on all the elements and mythological stories that I’m always inspired by from Aboriginal culture.”

The resulting ballet, called Rites, was a hit with audiences and critics Down Under, and a cultural watershed in its own right. The public here will have the chance to see it when the Australian Ballet and Bangarra (meaning “to make fire” in the Wiradjeri language of New South Wales) join forces in London next month.

The collaboration of such radically different companies represents a creative bridge across a painful historical divide. Composed of more than 600 nations, Australia’s Aborigines are said to have the longest continuous cultural history of any group on Earth. Yet the shadow of the Government’s shameful treatment of its indigenous population still looms large, despite this year’s public apology from the Prime Minister, Kevin Rudd.

To give some context, the Australian Ballet was founded in 1962, firmly embedded in a West European aesthetic. That was the yearthe Federal Council for Aboriginal Advancement launched a petition demanding a repeal of all discriminatory legislation. But it wasn’t until 1973 that the Migration Act made it possible for Aborigines to obtain a passport without also getting a special permit.

Bangarra is both much younger and far older than its classical counterpart. Composed almost exclusively of Aboriginals and Torres Strait Islanders, the troupe was formed in 1989 but, as Page is quick to point out, is able to tap into a treasure trove of indigenous dances, songs and stories that have existed for more than 40,000 years.

This rich heritage was Page’s bedrock when approaching both Stravinsky and the task of integrating dancers with such disparate styles – airborne, upright and marked by a purity of line in the case of Australian Ballet, and earthy, curved and at times even animalistic on Bangarra’s part.

Page says he aimed to “go along with what the story was originally, but implement my cultural inheritance about how the land shapes traditional people, their customs and their relationships with the environment and the creatures in it.”

He divided the score into sections corresponding to the elements, and parcelled these out to the two companies: “I thought Bangarra could handle earth and fire since they’re so close to our traditions, the ballet company could do wind and then I’d bring everybody together in the water section.” The sacrifice of the original ballet, when a young maiden – the Chosen One – dances herself to death, was replaced by a male initiation ceremony.

With its vivid, dynamically varied mix of serenity and ferocity, pointe shoes and bare feet, technique and instinct, the overall effect of Rites is at once raw yet refined. The performance is topped and tailed by short scenes, entitled Awakening and Dreaming, during which the companies also mingle and blend onstage. The Bangarra dancer Yolande Brown compares Awakening to “the first kiss of the sun on the earth in the morning”, while Dreaming represents “the end of the day, the year or some cycle of time, washing that away and purifying the journey so that maybe it can begin again somewhere else”.

The journey Rites offered was about more than aesthetics. David McAllister, the artistic director of Australian Ballet, was a company member when the piece was given its premiere in 1997 and danced in a later revival. “It was a profound time for us as an organisation,” he recalls. “I grew up in Western Australia, so there were a lot of indigenous kids at my school. But a lot of our dancers had never been close to indigenous Australians before, let alone danced alongside them. Before it started, I think we all thought it would be really strange having these two companies together. What we realised was that we have so much more in common than we’d ever imagined.”

In the bigger picture Rites was a timely reflection of Australia’s unresolved issues of reconciliation and reparation. According to McAllister, Page’s dance materealised “at a period in our history when there wasn’t as much regard for our indigenous population as there should have been. We have still got a long way to go. It was never meant to be a political work, but it was a beautiful metaphor for the way we should all live together – celebrating a shared vision rather than constantly bumping up against things we’ve done wrong in the past. That’s not just about Australia’s indigenous and European cultures. It pertains to people around the planet.”

Before Rites comes to London the dance will be presented in Paris, where Vaslav Nijinsky’s original version had its infamous premiere in 1913. “At first I was a bit frightened to go there,” Page says. “It would be great if Stravinsky’s spirit was able to review me: ‘Hey, I got booed offstage. Don’t worry about it.’ ” Joking aside, Page is healthily pragmatic about what he and Bangarra are about. “I’m not there to get a gold medal for choreography . . . At the end of the day I’m just a storyteller who’s grabbing the nuances of the spirit of where all the traditional forms come from.”

Rites, Sadler’s Wells, London EC1 (www.sadlerswells.com 0844 4124300), Oct 7-11; Australian Ballet’s Swan Lake, the Lowry, Salford, 14-18 (www.thelowry.com 0870 7875788), Oct 14-18

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