Jermyn Street Theatre makes a habit of rediscovering old works – in recent years, it's dusted down little-known plays by Maxim Gorky, Eugene O'Neill, and JB Priestley. Artistic director Tom Littler, who took over from Anthony Biggs last year, is maintaining the tradition, closing his second season in charge with Proud Haddock's production of Christopher Isherwood and WH Auden's rarely revived 1935 drama The Dog Beneath the Skin.

It's rarely revived for a reason. Isherwood and Auden's play is a curious thing – an episodic drama infused with poetry (yep, that's right, almost every line rhymes) that gleefully satirises the political landscape of 1930s Europe. Back then, maybe it wore all that well, but in 2018, it really doesn't. No matter how hard director Jimmy Walters huffs and puffs, he can't blow the cobwebs off this one.

The narrative follows Alan Norman (Pete Ashmore), a sprightly chap from the bucolic village of Pressan Ambo, who is chosen, Hunger Games style, to go and search for the long-lost heir of the local lord. Alan and his suspiciously humanoid dog (Cressida Bonas, on all fours in a fluffy brown jumpsuit) hop on a channel steamer and proceed to go gallivanting around Europe – interwar interrailing – on the hunt for the errant Frances Crewe. He witnesses a state execution in "Ostnia", gets tied up in a lunatic asylum in "Westland". "Is Francis Crewe, English, known perhaps to you?" is his chirpy refrain as he bounds from country to fictional country.

It's a pretty naked framework for Auden and Isherwood to take potshots at the creaky dynasties and authoritarian regimes of Europe in the 1930s, but it has entirely lost its bite since then. It's no longer clear which country is meant to be which, and why any of it is funny, and who any of the OTT characters is lampooning. The play is interesting historically, I guess, but dramatically? No, sir.

It's not the fault of Walters or his hard-working, multi-roling eight-strong cast, who throw themselves into a roster of caricatures with gusto – Edmund Digby-Jones is particularly sweaty come the curtain. Walters and designer Rebecca Brower embrace that scrubbed-up, vaudevillian, uber-theatrical aesthetic – twirling scene-changes, an ever-present piano, and simply loads and loads of chairs. It's cluttered, but it mostly works, countering the inherent pantomime-y lameness of the rhyming script.

Let's be honest. This is the kind of show that will appeal to Jermyn Street's core audience. One chap sitting next to me even complained that he hadn't been given his "usual seat". If you want to chase the grey pound, that's fair enough – they sign the cheques that keep the theatre open, after all – but if you're going to play to that particular gallery, at least pick a play worth reviving.

The Dog Beneath the Skin runs at the Jermyn Street Theatre until 31 March.