On the day I attended, there was a definite end-of-term feel to The Game’s A Foot, Try The Fish, a sly parody of 1930s detective fiction with strong echoes of Lord Peter Wimsey. The show was many things – witty, amiable, engaging – but a tight and polished performance it was not. At this stage of the Fringe, however, we’re all getting a little hysterical, and Tom Taylor’s improvised tomfoolery gave me the longest and loudest laughs I’ve had this August; more importantly, I can say the same about his wisecracking, neatly self-referential script.

The story revolves around the aristocratic Charlie Montague, who’s inspired by an incident involving a cockatoo and a tuba to “have a crack at this detective what-not”. Montague is a likeable protagonist, foppish yet ironic, and soon finds himself embroiled in a convoluted mystery set in a luxury seaside hotel. Taylor plays all the other characters as well, leading to plenty of that comedy-theatre staple – darting around the stage to hold discussions with himself – alongside some entertaining practical challenges, and a vast array of truly terrible accents.

Taylor’s a former finalist in So You Think You’re Funny?, and he has the comedian’s instinct for drawing sustained humour out of things that aren’t, on the surface, particularly promising. The first reference to a body “flopping down the stairs” is amusing at best, but Taylor repeats it – without it ever seeming forced – until each subsequent mention becomes even more hilarious. He pokes plenty of fun at himself too, with frequent and creative references to his own show’s distinctly low-rent production values.

The detective-fiction parody is affectionate and the storyline, though pleasingly overblown, never becomes ludicrous. It is, in fact, a perfectly serviceable Golden Age mystery, with clues you feel you should have spotted and a satisfying solution at the end. If you like your Agatha Christie, or particularly your Dorothy L Sayers, you’ll enjoy the substance beneath the humour and the frequent nods to detective fiction tropes.

I absolutely loved every moment of it – but if I’m honest, it could have been even better. The characterisation of the minor figures is more grotesque than it needs to be, and Montague – though well-realised and always entertaining – grows a little one-note after a while. Intentionally bad acting is very much part of the joke, but at times I felt it was holding Taylor back, inhibiting the subtler, more rewarding humour a proper treatment of his characters might reveal.

So there’s room for it to be slicker and a whole lot tighter, but this is already an astoundingly funny show. With a solid plotline as its foundation – and just the right amount of parody balanced on top – this locked-room mystery told in a cut-glass accent is an intelligent but uncomplicated pleasure.