"Let's take our valley back, boys." Three scowling farmers, shotguns in laps, sit on a hill, waiting. They're out to rid their land of vermin: the Fantastic Fox family living off their hard farming for years, snaffling produce to feed their friends. "Before you know it," sneers one, "you don't even recognise your own countryside."

With a little tinkering here and there, Roald Dahl's novella has blossomed into a sharp political satire for our times – three old English farmers outfoxed and foxed off. Sponged off and outsped, the poultry producers, Boggis, Bunce and Bean, form a countryside alliance to take back control. Having tried their luck with shotguns – only succeeding in blasting Mr Fox's tail off – they return in diggers and lay siege to his foxhole to starve the family out. In response, Mr Fox and co. dig deeper – burrowing all the way to their storage barns.

Set to an eclectic Arthur Darvill songbook, Sam Holcroft's adaptation extends Dahl's fable into a fully-fledged plot. She's given the Fox family a whole bunch of furry friends – Gruffud Glyn's blind mine Mole, Raphael Bushay's methodical Badger and, best of all, Sandy Foster's eager-but-empty-headed Rabbit – and next to them, Greg Barnett's Mr Fox seems all the more fantastic.

In an orange shellsuit, go-faster stripes on his streamlined ears, he's a preening, posturing vainglorious egotist. He might share his pickings, providing for all, but he won't share the load. Only without his tail, he's not the fox he once was.

Holcroft is particularly attuned to the politics of all this, and Mr Fox becomes two things at once – the skivers of broken Britain and the slickers of the liberal elite. His rampant individualism breaks the system, just as an elite has run neoliberalism ragged. Tom Scutt's design turns the world into a game, with critters in sportswear and pixelated Minecraft-style produce, but the farmers' all-too-real threats make the life-or-death cost abundantly clear. Richard Atwill's Bean is particularly chilling: a cold leer of a man with a Schindler's List haircut. No wonder the animals go to ground.

Trouble is Maria Aberg's show doesn't quite know what it wants to be. Neither entirely a musical, not a play set to song, it's most like a variety show strung along to a plot. Holcroft's script is episodic – each factory invasion a routine of its own – and Darvill's songs don't always move things along. As such, it bunny hops where it needs to take flight; weighed down, ultimately, by a real lack of wit. Despite four separate lyricists, only a handful of lines land their laughs.

Nonetheless, there are pleasures aplenty. Darvill delivers a few cracking numbers – an angry-Hendrix spoof as the three farmers find their inner-fox and a rogue rat's hymn to self-interest that swerves from cheery dance-hall to chaotic punk as the cider sets in. The singing's just short, though, and without musical theatre actors, what's gained in character gets lost in showstopping aplomb.

The cast do fill Scutt's sporty costumes brilliantly, though. Glyn's mole gawps, blind beneath his pink crash helmet and back-to-front cricket gloves, while Foster's bunny, in lyrca and legwarmers, is like a lobotomised Olivia Newton-John, more physical than intellectual. In they end, they all play their part. "Every creature," as Mr Fox preaches, "has its purpose."

Fantastic Mr Fox runs at the Nuffield Southampton Theatre until 8 January, then the Lyric Hammersmith 25 January to 18 Febuary, before embarking on a UK tour.

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