Alice in Wonderland uncaged: ZooNation are giving Lewis Carroll the hip-hop treatment

The Royal Ballet's skylit studios at the Royal Opera House always host intense work-outs by dedicated dancers. This time, though, the walls are shaking. The ZooNation Dance Company are rehearsing its new, Lewis Carroll-inspired family show, The Mad Hatter's Tea Party. Next door the ballet principals are tackling Christopher Wheeldon's Alice's Adventures in Wonderland for the main stage, but in here the explosive energy of street dance conjures a very different take on Carroll's zany characters for the Linbury Studio's Christmas offering.

It is the first time the Royal Opera House has commissioned a show in hip-hop style – and given the runaway success of ZooNation's larger-scale productions, expectations run high. The first, for instance, was Into the Hoods, originally commissioned by Sadler's Wells, it transferred to the Novello Theatre and became the longest-running dance show in West End history.

Kate Prince, artistic direction of ZooNation, has spun a new story out of Carroll's characters: they are in a mental health institution ("We're all mad here," as the Cheshire Cat says to Alice). Ernest, their therapist, tries his best to help them, but cracks under the strain. Catatonic, he is kidnapped by his charges and carried off to Wonderland.

It sounds dark and off the wall, but the studio is crackling with laughter and horsing about, quite unlike the hierarchical quiet of a ballet rehearsal. "If you don't get on with it, you'll be late for lunch," Prince reminds her cast from the director's table. But the spirit is not as anarchic as all that. The freedom to joke lets gags for the show evolve naturally, and the collegial atmosphere – with a different dancer leading the choreography for each number – lets everyone learn from one another's strengths. In the end, hard graft and discipline permeate everything these dancers do, no matter their style.

The dancers say they are thrilled by their new surroundings. "We love it!" they chorus. "The kind of expertise we're working with in every department is on another level," Prince adds. As for the Royal Ballet dancers, she says that occasionally they have appeared at the studio door to look on longingly – but had no time to join in before their own rehearsals.

"They're already in the studio when I arrive for class, working hard, and you hear their music going all day long," remarks Steven McRae, the Royal Ballet's principal dancer and the original Mad Hatter in Wheeldon's Alice. He has had a "dance-off" for a promotional video – coming soon to YouTube - with ZooNation's Mad Hatter, Turbo (Isaac Baptiste), well known to TV audiences as a finalist on Sky TV's Got to Dance and in Turbo Boost on CBBC. McRae's Mad Hatter tap-dances; Turbo, he says, "was standing on his hands and doing crazy things!"

In place of pointe shoes and leotards the ZooNation crowd are in trainers, long, loose tops and baggy sweatpants, and there's some vibrant body art on show. And instead of the poised, upward focus of ballet, here everything is rooted in the ground, unless it involves handstands on the edge of the tea-party table.

Many of the 11 dancers have dipped a toe into ballet, often picking a direction after early training in eclectic styles. Tommy Franzen, the dazzling, Olivier Award-nominated Swedish dancer who plays Ernest, has appeared before at the Royal Opera House (in Goldberg): "I used to take the morning class with the ballet company several times a week," he says.

Lizzie Gough, who dances Alice, remarks: "I'd always wanted to be in the ballet. But I'm still here – in another way!" She had an intense training in musical theatre and has tried everything from jazz flamenco to Bikram yoga: "I sort of fell into street dance," she says. Teneisha Bonner as the Queen of Hearts, like Gough has been a ZooNation star from the start and has a huge range of styles under her belt. "I started dancing very late," she says, "but I never looked back." Being a dancer is a question of discipline and expertise, no matter the genre, and mutual respect is the order of the day.

Despite their huge success, though, there can be an extraordinary degree of misunderstanding in the world at large about what ZooNation is and what it does. "We were described in one newspaper as a 'rap outfit'," Prince says. "We're not a rap outfit and we're not a 'gang'. We're a dance company that tells stories for a family audience. They are always funny and they always have heart."

The name "ZooNation" might conjure up images of dancers unleashing their inner wild animal. Wrong again. "Years ago, I went to the Edinburgh Fringe with a theatre company and we needed a name," Prince says. "All the companies were listed alphabetically in one programme, so it was best to choose something beginning with either A or Z. We went with Zoo Theatre Company. When I founded the dance company in 2002 I kept the Zoo – and I was such a Janet Jackson and "Rhythm Nation" fan that I decided to call it ZooNation!"

The Mad Hatter's Tea Party is the latest of the Royal Opera House's innovative Christmas shows in its Linbury Studio, led by ballet and opera in alternate years. Given the usual shortage of seasonal family choices beyond The Nutcracker (which the Royal Ballet is not doing this year), this is a welcome initiative and has resulted in some major success stories. The Wind in the Willows, choreographed by Will Tuckett for the Royal Ballet, has done so well that it transferred to the West End, won an Olivier Award this year and is currently enjoying an eight-week revival at the Vaudeville Theatre. If ZooNation's contribution can take off similarly, everyone stands to benefit.

It is certainly not a case of using a subsidised company to fund commercial shows – "Rather the other way around," says the Royal Ballet's artistic director, Kevin O'Hare. "If we've commissioned a work and it does well, then a percentage comes back to the company. The Wind in the Willows went so well that we're hoping we can repeat that success.

Commissioning ZooNation is largely about opening up the theatre's spaces to new types of dance and dancer, with broadened audiences to match. Still, these are straitened times for everyone. If a commission like this can refresh the repertoire and its fans, create cutting-edge new work and achieve widespread commercial success in one fell swoop, that could mean Christmas cheer for all.

'The Mad Hatter's Tea Party', Royal Opera House, London WC2 (020 7304 4000) Saturday to 3 January