If Twyla Tharp made cars, she’d make big, shiny American convertibles. They’d be growly Mustangs, or sleek Corvettes or one of those Alpha Romeo Spiders (admittedly an Italian car, but as Dustin Hoffman drove one in The Graduate, it’s American in spirit if not in design). Of course, Twyla Tharp doesn’t make cars. She’s a renowned choreographer who mixes high art with pop culture, ballet with street dance, Bach with Chuck Berry. But she is as thrilling to watch as driving one of those glorious soft-tops.

Dance world insiders have always loved Tharp’s hi-lo mix, her clever blending of triple pirouettes and shadow-boxing, the arabesques and “so what” shrugs, the way she revs it up, crosses everything over and makes us laugh and cheer at the fun of it all. Now, thanks to Movin' Out, the Broadway transfer that moves in to the West End’s Apollo Victoria this week, a broader audience is joining in. And you can’t help but sense that Tharp is experiencing the cross-over of her career.

“I think of it as a chronicle of American history,” Tharp says of the Tony award-winning show that’s part ballet, part musical, part rock concert and 100 percent Broadway hit. Set to a selection of Billy Joel pop hits, from “Pressure” and “Uptown Girl” to the title song, Movin' Out follows five high school friends over twenty-odd years from pre- to post-Vietnam.

Billy Joel gave Tharp, who directs and choreographs, carte blanche with his music. “He was amazing,” she recalls. “Billy said, ‘Go for it.’ I said, ‘You’re kidding?’ He said, ‘No, I mean it. Take what you need.’ And I said, “I need all the music.’ He said, ‘You got it.’”

Joel is equally complimentary. “I’d been approached before,” he says. “People would say, ‘Let’s make ‘Piano Man’ into a show.’ But I always turned them down. Twyla was different. She showed me these beautifully choreographed dances, and I thought, ‘This is a great new genre for my music.’ And I said to her, ‘Go ahead.’”

So go ahead Tharp did, converting Joel’s anthems and ballads into a new type of dance show. The story, Joel explains, “is based on the lyrics of my songs. The dancers are the characters in the tunes, Brenda and Eddie, Judy and James. Twyla took my characters and brought them alive. She asked me, ‘What happened to Brenda and Eddie?’ I said, ‘I don’t know.’ Twyla let them go on with their lives. And I was as interested as anybody to see what happened.”

Movin' Out is their story told through 24 of Joel’s songs and some truly powerhouse dancing. Style-wise, it is signature Tharp, a hi-lo combination of classical and street moves, with balletic arabesques piled on break-dancing spins, followed by sweet love duets and big group dances that somehow gather everyone together and make sense of their emotions.

“I always, somehow, knew I was going to dance,” says the Portland born, California-raised Tharp. “I had dancing lessons of every sort. Ballet, baton twirling, Hawaiian tap. I was interested in becoming a show dancer, for which I was not tall enough.” Or cute enough, the seriously petite woman might have sighed. “I auditioned for the Radio City Rockettes. They said, ‘We love your fouettes, but can’t you smile?’”

Undaunted by rejection, the ambitious young Tharp moved to New York and studied with the modern dance legend Martha Graham – a huge cross-over if ever there was one. She soon started creating her own work and in 1965 formed her own company that challenged just about every theatrical convention. Tharp’s “ballets” featured non-dancers, they were performed in non-theatre spaces and they didn’t use music – all considered hugely radical in the 1960s. But despite challenging the mainstream, the mainstream was to give Tharp her first real break.

In 1973, the dancer-director Robert Joffrey invited her to work with his ballet troupe and the result was Deuce Coupe to Beach Boys songs. It was both massively successful and a cultural turning point. Tharp’s Deuce Coupe was one of the first cross-overs between modern dance and classical ballet, giving the ballet dancers new moves and the choreographer new dancers. It was also, to anyone’s knowledge, the first time someone had thought to combine ballet with tunes about the vintage two-door deuce coupes that were the must-have sedans of 1950s hot-rodders.

But for Tharp, the mix was natural. “A lot of people insisted on a wall between modern dance and ballet,” she once said. “I’m beginning to think that walls are very unhealthy things.”

After Deuce Coupe, commissions came thick and fast, including a fabled collaboration with Mikhail Baryshnikov. For the Soviet defector, Tharp created When Push Comes to Shove, a dazzling showpiece that turned the serenely elegant ballet dancer into a skirt-chasing rogue – although some say she just showed him as he was. Tharp also choreographed for the ice skater John Curry, worked in film (including the Mozart biopic Amadeus), and in the 1980s had a big-wig job at American Ballet Theatre. Link-ups with other blue-chip ballet troupes followed, as did a collaboration with Talking Heads’ David Byrne, plus more pop and jazz, from Fats Waller and Supertramp to Bruce Springsteen, Paul Simon and Frank Sinatra.

Bach to Chuck Berry, hot-rodders to ballet dancers, ice skating to movie making: Tharp’s career is one long series of cross-overs, and as every bit of a mix as her new show. But what connects all her work, what makes it recognisably her own, is a deep sense of America, with all its energy and contradictions, and its multi-culti mishmash. What Tharp loves most are American teenagers: their optimism, their loss of innocence and the solace they find in friends. And she’s captured all of this in Movin' Out.

Truth be told, it’s not an original story, but Tharp has distilled its spirit with feeling and flair. “It’s a confirmation, a positive,” she believes. “There is darkness to this, but ultimately it’s optimistic. I let us come home.”

The lady herself doesn’t say so, but you suspect the homecoming will be in one of those big, shiny American convertibles.

Movin' Out starts previews on 28 March 2006 before opening on 10 April 2006 at the Apollo Victoria (0870 4000 889).