This musical has almost nothing to do with the 2009 David Fincher movie of the same name. It doesn’t even have much in common with the original 1922 F Scott Fitzgerald short story on which the film was based. All it shares is the central conceit of a life lived backwards – a human born as an elderly man who regresses to infancy over the course of his three score years and 10. And, for all its flaws, the show tells this story – using puppetry, smart staging and some fine musicianship – rather more effectively than Brad Pitt and co managed.

Jethro Compton’s production relocates the tale to a Cornish fishing village, starting in 1918 and moving towards the 1980s. The setting is an excuse to turn the story into a Celtic-themed musical and, much like the cast’s wardrobe, Darren Clark’s original songs have a touch of the Mumford & Sons about them: rather nondescript, blandly anthemic ballads dressed up as folk songs, with a couple of earworms that succeed in setting the tone.

What brings this production to life is the inspired staging and the remarkable performances. The tight five-person cast – James Marlowe, Matt Burns, Rosalind Ford, Joey Hickman and Philippa Hogg – do everything between them. Each takes on multiple roles; they sing perfect harmonies, manipulate puppet characters, and play at least two instruments from an assortment of violin, cello, piano, guitar, trombone, accordion and drums.

It was probably unwise of Compton to direct his own script – a second pair of eyes might have trimmed half an hour of flab – but this version lingers on some aspects of the story unexplored by the film or book. A woman giving birth to an elderly man is not presented as some surrealist thought experiment but as a traumatising experience, while the protagonist’s dilemmas are heartbreaking rather than whimsical. Even when Button is being played by a junkyard puppet – as he is at the start and end of the show – he elicits empathy. It’s a freak show that humanises the freak.

• At Southwark Playhouse, London, until 8 June