Murders, and murderers, seem to fascinate us all. We can't get enough of true-crime stories – the more gothic and grisly the better. A couple of centuries ago, we'd have scratched that itch by attending public hangings; in this more enlightened age, we simply go to Fringe shows. Brighton, Queen of Slaughtering Places is well aware of that irony, gently critiquing its own genre even as it tells a satisfyingly bloodstained tale.

And that's a bold move from playwright Nigel Fairs, who's made a veritable industry over the past few years from scripts based on notorious local crimes. This time round he's tackled the Brighton Trunk Murders, a bizarre series of events in 1934 which saw a cluster of dismembered body parts discovered in packing chests around the city. Fairs' script is anchored firmly in Brighton; clever references to the ever-changing landscape reinforce the sense of place and time, and there are subtle nods to the unusual venue we find ourselves in, a subterranean room in the old police cells themselves famed for a Victorian-era murder.

The story's told at first by Tony Manchini, the only man directly implicated in the 1930's killings. Actor Michael Chance fleshes out his character well: on the surface he's a likeable chancer, but a hint of menace lurks just below. He relishes his notoriety, and the chance to milk his grotesque tale – but there's someone here who's determined to spoil his party, to harry him with questions and point out his story's flaws. The ensuing interview-like format isn't the most nuanced device in the world, but it serves well to narrate the story, and get those of us who don't know the history quickly up to speed.

Because there are other stories we need to move onto. There's a squalid little tale from a century before, and an unsolved case from Manchini's time – both of which feature bodies in chests, and pose a threat to his crown as the Brighton Trunk Murderer. The nineteenth-century tale is told with relish, complete with a body hanging from an improvised butcher's hook; but the third case is different, closer to our time and easier to relate to. Sally Paffett is convincing as the unidentified victim, and the uncomfortable realism of those particular scenes – more harrowing than macabre – sets us up for an unexpected and thought-provoking conclusion.

They don't exactly break the fourth wall, but the actors do drop hints that they're acting – quietly at first, but more and more clearly later on. For a while I resented these intrusions, but I came to understand that there's a very real purpose to them, a purpose which elevates Fairs' script above the majority of true-crime tales. Again the exposition lacks a little subtlety, but Fairs has the actors deliver an interesting challenge: an invitation to reflect on why certain murders fascinate us, and on whether that points to something we aren't quite facing about our own approach to the world.

I'd expected Brighton, Queen of Slaughtering Places to be a guilty gothic treat – and against that brief, it duly delivered. But it gave me something more surprising too: a thought-provoking test of my own motivations, perhaps even the gentlest of rebukes. It uses our fascination with an iconic crime as an opportunity to hold up a mirror… and that introspection, it turns out, yields a chilling satisfaction of its own.