Hans Christian Andersen's story about the little match girl freezing to death on New Year’s Eve has sparked an extraordinary cabaret of sacrifice and salvation from the Australian diva Meow Meow, whom we last saw in London in The Umbrellas of Cherbourg.

This seasonal special on the South Bank originated at the Malthouse Theatre in Melbourne, where Meow Meow devised the show - which is set on a huge red bed beneath a giant chandelier - with director Marion Potts, performer Chris Ryan and composer Iain Grandage.

She's like a bizarre mixture of Bette Midler and Fenella Fielding, belting out her numbers with great attack and sudden vulnerability, racing round the auditorium, even ripping off one of the exit signs to sing by its livid green light, achieving transcendence by actually wearing the chandelier as she rises to the roof.

Obviously Hans Christian Andersen's agit-prop fairy tale, as she calls it, is a leaping off point, not a faithfully observed source. It's as though Meow Meow has thrown herself on our charity and indulgence, rather as the little girl in the story is abandoned to the cruel night air, warming herself by the glow of the visions she sees in the flickering light of the last of the matches.

Meow Meow's matches are the songs she sings, ranging from her own and Iain Grandage's emotionally garish compositions to some heart-warming blockbusters by Megan Washington, Serge Gainsbourg, Noël Coward, Laurie Anderson and Patty Griffin.

It's a rich and unusual musical roster, but it's held together by the tempestuous force of her personality, the seeming limitless possibilities of her vocal talent and a sort of skittish, camp flamboyance that is almost too much to be contained in a single theatre show.

Lance Horne's musical direction and Paul Jackson's lighting create some magical effects so that Meow Meow can achieve the waif-like tenderness in the story while maintaining her own theatricality. You hear distant strains of Purcell, or Wagner, and the stage is suddenly an empty street of guttering candles.

But Meow Meow doesn’t just reach for the stars. In the words of one her own songs, she tears them down, and an audience will be left not dabbing their eyes but stamping their feet and demanding an encore. The little match girl goes up in flames.