‘I’m not special,’ says the woman in the spotlight, all chairs pointed at her, in a glamorous art deco bar in Central London. We’re not expected to believe her, and she doesn’t really believe it herself.

But Holly Burn is trying to wean herself off the addiction to her own legend. She’s from Generation Y, an entitled child of the Eighties who was told she was unique and fabulous and talented – and could be whatever she wanted.

Whatever she wanted was to be on stage at the Carnegie Hall with Barbra Streisand… Why has she not got her birthright? She clearly maintains she is special, it’s just that the rest of the world hasn’t cottoned on yet… but also acknowledges that the easy life might be a pipe dream now thirtysomething reality has setting in.

But the sense of showing off and needing to be the centre of attention has never left her. She starts the gig like a manic dinner-party host, introducing herself to the audience at their tables, before draping herself awkwardly across a grand piano, a reminder of the jazz and cabaret nights this elegant room in Zedel usually hosts, and of the life she always dreamed of.

She tries to be a sophisticate, but she can’t help but play the clown. Much of this is the comedy of ‘dicking about’ as she inexpertly dabbles in kabuki theatre, addresses a stuffed parrot, or stars doing stretches on stage, just to be in the moment. ‘Special’ has a more euphemistic second meaning, of course, and Burn is certainly peculiar.

It means the show can be hard to get a handle on, even that central idea proving deliberately slippery, as she’s clearly not ready to give up that feeling of eminence imbued in her by her parents. Parallels between her four-year-old self having her every whim accommodated, and a helpless Hollywood starlet demanding the same of her frazzled assistants, is a well-made joke. But in many ways,she hasn’t matured from a kid putting on an amateur show for her folks: that’s the loose vibe she’s putting across, even though there’s a robust structure underpinning this.

She does know, however, that the Generation Y dream was just that: You can’t have it all. You can’t pull off that flighty Amelie/Audrey Hepburn nonsense in the real word, so Burn just has to imagine it. In one of several reveries, she dreams of a romantic fling with a pilot, and the sensual devouring of nectarines in the Tuscan sun. In another imagines herself smoking elegantly on a New York rooftop before falling into a skip.

You can tell from that description that although her mania calms down,the show keeps strong elements of weird. Burn is blessed with funny bones (and a cracking singing voice, it turns out) plus a charisma that makes the audience want to stick with her from oddball sketch to oddball sketch, even in the moments where the odd narrative goes off the boil. 

I Am Special is a performer at play. A show, you feel, that’s for her as much as us. You’d probably never be able to knock her peculiarities into anything like a conventional show – and she wouldn’t want to. Because she IS special.