His eyes brooding like a full-beam laser of charisma, Rudolf Nureyev makes a fascinating, pulsating subject for a new documentary by the award-winning sibling pair of Jacqui and David Morris.

It’s a beautiful yet fun biography, taking all the major steps in a career that spanned the world yet was tragically extinguished by AIDS in 1993 at the age of just 54. I know, I was as shocked as you to hear that.

The centrepiece of the show is, of course, his relationship with Margot Fonteyn, an unlikely partnership between a prowling panther and an exquisite bird that somehow transformed ballet into the hottest ticket in swinging London during the 1960s. “Forget Beatlemania,” opines one expert in voice over, “this was Balletmania.”

There’s a lovely bit of news archive showing the tiny post room at the Royal Opera in Covent Garden overflowing with fan mail, and dutiful clerk tipping yet more sacks of it onto deluged desks. Outside, screaming fans awaited Nureyev. Inside, the encores and curtain calls went on for as long as an hour.

It must have been quite something to witness the pair perform Swan Lake, or Romeo and Juliet, and the archive film is used beautifully here, reflecting the story of their mutual affection. “We moved with one body, one soul,” he says.

Fonteyn considered herself to be past her prime at 40 and didn’t want anything to do with this 21-year-old hot Russian who, just a few months earlier in 1961, had leapt into the arms of the gendarmes at Orly airport and become the first big name defector of the Cold War. It should be on surprise, points out the film, that barely two months later, the Berlin Wall went up. Nureyev could probably have leapt over that, too.

Before Fonteyn, he’d been a major star in Soviet Russia, a phenomenon who’d left the dead end town of Ufa in the Urals and the beatings of his soldier father (“he didn’t want a cissy for a son”), to travel to the Kirov in St Petersburg. Like cosmonaut Yuri Gagarin, he was held as the symbol of the new Russian idol, an artist the West couldn’t possibly match.

The defection scene is breathlessly retold; the Fonteyn years thrillingly recaptured; the sheer personality of this dancer re-created on and off-stage, through appearances on Parkinson and, in the US, the Dick Cavett show where he’s received like a rock star, albeit one in thigh-length brocade boots.

His homosexuality is dealt with, too, although through the modern prism of what we now call “fluidity” – but of course, as events move into the late 70s and he moves to New York to dance with Martha Graham’s troupe and reside in the Dakota building, the spectre of AIDS begins to haunt the picture.

Rudolf ends up in Paris, his stentorian approach revitalising the Opera de Paris and restoring it to former glories. All the time, his health is fading, yet it doesn’t prevent even more extraordinary drama in his personal life, including a return to Russia and some amazing reunions.

To reveal any more when reviewing such a film is to indulge in spoilers. Best let the story unfold and the memories be jogged, and let the music and the movement transport you. This was an extraordinary life that lived and breathed its art and this is a lovely, lively, joyous film that lets the beauty of its subject speak – and dance – for itself.