We are in the mysterious town of Schwartzgarten. You may not have heard of it, but it is big enough to have its own opera house and a reformatory for disobedient girls.

Tatiana is a child who may very well end up in that reformatory. Fixated with death, she spends her days designing tombs and trying to keep the cat she rescued from drowning – given the name Count Frederick Sebastian – from either killing the canaries owned by her neighbour, esteemed opera singer Mrs Stein-Hoffelman, or bringing home rats for the table. The scrawny cat (a very unappealing puppet brought to life by Richard Booth), at first happy enough to have a bowl of food, soon turns his attention to the other living things he can find.

For Tatiana's widowed father, inventor Maximillian Dressler, Mrs Stein-Hoffelman (who has buried four husbands) could provide the finance for his strange inventions, particularly a mechanical brace that would enable Count Frederick Sebastian to walk upright and eat with a knife and fork.

What sounds like a Gothic horror which may have emerged from a Slavic state in the 18th century is actually a new work by Christopher William Hill and it would be easy to give a post-Trump, #MeToo interpretation to the story. Or you could simply see it as a horror farce in which a lot of canaries die and one actor (Christopher Staines) plays the opera singer, a detective, an undertaker and a solicitor at break-neck speed.

Natasha Jenkin's complex Dressler home allows the play to hit the ground running – there's a metal meat safe and a samovar, a typewriter and a telephone, and lots of books, family ephemera and (for good measure) a graveyard. All of which creates a weird atmosphere for our story.

Tatiana (Charlie Cameron) and her father (Dominic Marsh) are struggling to survive, so it's best not to ask what's in the goulash. The girl has a good heart and protects her father by playing the role of a dependent child. But she's growing up fast and has caught the eye of Franz (Jeremy Ang Jones) who delivers parcels to the house.

Hill's play may be an acquired taste but it's a popular genre – remember the dark Get Out was a surprise cinema hit last year. Luke Kernaghan directs Clockwork Canaries like a farce but there are darker layers underneath which are planted in the mind for the audience to dig up later.

Clockwork Canaries runs at The Drum, Theatre Royal Plymouth, until 10 March.