The fringe is nothing if not a place where unknowns can write their names across the stars. Ayoade Bamgboye does so in a matter of moments in her debut show, Swings and Roundabouts, which makes instantly clear that, wow, here’s a voice you can’t help but listen to. It’s a slippery one, mind you: the show is delivered now in a Nigerian accent, now in BBC Radio 4 RP, with no guide to the shifting register. It’s ticklishly destabilising, and wholly justified by a show tracing the Londoner’s journey (cultural, geographical, even metaphysical) from Africa to the UK.

That makes it sound like a conventional fringe debut, but it’s not, or at least, not to begin with. Thrillingly, Bamgboye pitches us straight into Swings and Roundabouts – no context, no handrails – with a giddy story about eavesdropping on a quarrel in a Co-op. Her command, the confidence in her delivery and how she makes the whole room her own, is quite something. There’s no point denying that the set then reverts more to fringe-rookie type, flashing back to the story of where Bamgboye has come from and who she now is. In our host’s case, that’s an oldest (or in Yoruba culture, youngest) twin, unusually interested in the circumstances of audience members’ births, with a name meaning “crown of joy” and a superiority complex to match.

A move to the UK in her twenties knocked that joy out of Bamgboye, though; one routine here workshops English terms for misery. Her outsider eye for native British idiom surfaces throughout the show, helping pep things up as its lost-soul protagonist turns to God (“I gave my life to Christ. He gave it right back”), loses her father (cue a lovely supermarket metaphor for parental bereavement), and turns to the Samaritans. None of this is downbeat – it’s a show characterised by bright thinking, vocal variety and the kind of dizzying hairpin turns (into song, into sudden dramatic monologue) that explain why her therapist compared her to Jim Carrey. The impression is of a live-wire artist making up her own rules, and as striking a debut as I’ve seen at this year’s fringe.