Mark Ravenhill’s presentation of drag queen Bette Bourne is an unusual rough and tumble of a small show: a sort of This is Your Life as a mock spontaneous chat between friends, and it’s very charming.

But it’s also rather too flaccid, and doesn’t quite match the confessional reminiscences of Quentin Crisp in either the beguiling asperity stakes or as a statement of heroic defiance.

Bette, who first acted with his given name of Peter, is a gentle old Cockney drag queen with a sudden sorrow for all the friends he lost to AIDS in the mid 1980s and a gentle acceptance of all that’s happened.

But his story is fascinating and important, from life in rep – at the Old Vic in Robert David MacDonald’s version of War and Peace and with Ian McKellen in Marlowe’s Edward II – to Gay Liberation days in the Notting Hill commune and his famous Bloolips fringe company in London and New York, where he made a major impact on the gay cabaret scene.

The show was seen at last year’s Edinburgh Festival in three hour-long segments but has been condensed to just under two hours including an interval, which may account for the constant scrabbling between pages and over-relaxed air of what happens next.

We see pictures of Bette at school in Hackney, on the streets of Soho, on the model’s couch, in the thick of New York, and we hear a touching recording of his mother singing Gounod’s Ave Maria. His father apparently beat him up violently, but they managed a relationship of sorts towards the end.

Best of all, Bette removes his specs and gets to his feet – in a glittering tunic, long grey hair tied back in bunches like Anna Carteret – and sings Bessie Smith and an item from Neil Bartlett’s Sarrasine in an expert throwaway style that could be usefully applied to the rest of the show.

Ravenhill, in a checked shirt, jeans and pork pie hat, enjoys the proceedings as much as the rest of us but, as the director, he needs to tighten and squeeze, without losing the unusual air of practised informality, before the show goes to New York next month.