A pirate radio station is a clever subject for a jukebox musical. And there’s none more famous than Radio Caroline, whose revolutionary broadcasts from a boat off the Essex coast launched a culture war with the British government.

Writer Vikki Stone has partly fictionalised the story of that ship, with characters only tangentially based on the people – record-spinner Tony Blackburn, Irish businessman Ronan O’Rahilly – it made famous. Instead we have Robbie, a young man struggling to make his way until his love of pop lands him a DJ job, and his childhood sweetheart Caroline, supporting his dreams until she finds herself losing him to the boat of the same name.

A talented actor-musician cast deliver the show with rebellious energy and Jake Halsey-Jones and Claire Lee Shenfield, as Robbie and Caroline, match an endearing chemistry with charming vocal performances. Numbers by the Beatles, the Rolling Stones, the Kinks and more, impressively showcase the ensemble’s multifarious instrumental skills and are perkily choreographed. The Beach Boys’ Wouldn’t It Be Nice comes with magnificent backing vocals, and there’s a glorious Twist and Shout that literally rocks the boat.

The narrative, however, needs tightening. We spend a lot of time watching the pirate station’s founders, Declan and Kitty, laboriously talk us through their fight to keep the boat afloat, and few musicals can ever have made so much mention of the Isle of Man’s legislative body, Tynwald. As the caustically uptight postmastergeneral seeking to sink their business, Gareth Cooper punctuates the longueurs with valuable comic relief, and decries the American materialism seeping into society. “Don’t let it make you moist, Nigel!” he barks at his aide.

Stella Backman’s design, with its seaside bench and rusting pier, underscores the story’s empathy, and the “ordinary” Caroline who this 60s music was meant for. An opening prologue, mentioning Spotify, Napster and MP3s, aims to place the episode within a people’s history of music, and there are a few mentions of free speech, some from a surprisingly radicalised Robbie. But it’s never quite clear what point Stone’s show is trying to make – except that pirates have all the best tunes.

• At New Wolsey theatre, Ipswich, until 2 May. Then touring until 20 June