Satyrs were followers of the wine god, Dionysus; half-human, half-goat, all mischief. Onstage, they were more like half-man, half-penis. They ran around with lumbering, foot-long erections, encapsulations of all of our baser instincts. They boozed. They bonked. They basically just dicked around.

None of the ancient Greek satyr plays survived in full. Tragedy and comedy, yes, but not these raucous, hybrid affairs; subversive as satire, but rowdier, earthier, more Bacchanalian than that. We only know of them through secondary sources, depictions on vases or written accounts (God bless Greek theatre critics), but we don't have the texts themselves. They are lost to time. Culture gone missing.

It's a point Tony Harrison's extraordinary verse play pulls into the present. The Trackers of Oxyrhynchus is a mock satyr play. Its first outing, in 1990, remains a highlight of National Theatre history, as a dozen actors with beards, boners and tails rampaged around the Olivier. Harrison put them in clogs, to stomp up a storm, and in doing so, his play draws a thread from one lost art-form to another. It is a clarion call against the marginalisation of working class culture; one that feels all the more pressing today, albeit it arguably too little, too late.

Trackers starts with two Oxford dons, Bernard Grenfall (Tom Purbeck) and Arthur Hunt (Richard Glaves) sifting through scraps of papyrus in Egypt. Searching for fragments of Sophocles' lost satyr play, Ichneutae, they chuck out daily petitions in search of high art. Purbeck's cream-suited, cut-glass academic cuts an increasingly manic figure, until, one night, he's possessed by Apollo, god of music and poetry, who summons the satyrs to find his cattle.

They are quite something, the satyrs. Even only six-strong, Jimmy Walters' chorus fill the small space of the Finborough: their felt cocks flopping about between their legs; their clogs clattering into the ground. Harrison's play contrasts words with bodies: the nimbleness of his verse slams into the thomp of their feet. It's fair to say, the shoes have it.

But the writing is mighty satisfying too – unfussy in its rhythms, but no less smart for that, and witty in its rhymes. It swerves from elegant expression to bawdy asides, and, in sitting the two together, pushes against the "unbridgeable split" of high and low art.

The satyrs are ultimately shut out of high art, and wash up in shellsuits, culturally disenfranchised and more destructive than creative. When they turn on their leader Silenus (Glaves), Walters has them pull out their phones to film the attack.

His staging is gnatty and homespun, yet thanks to Amy Lawrence's clog choreography, carries a charge. Nonetheless, it makes you itch to see Harrison's play at full strength, with enough scale and space for its satyrs to run wild. Purbeck has a haughty intensity as Apollo, finding a real fluidity in both words and physicality, but its Glaves' Silenus, raging against the gods and the elite, who puts fire into its belly and gives it some balls.

The Trackers of Oxyrhynchus runs at the Finborough Theatre until 28 January.