Mute singers are not uncommon: people who can't speak, but can sing. This new British musical gives us a vocalist who's lost his voice entirely. A few years ago, Michael was a promising indie musician, half of a duo called LostBoy, but he's been shut up in his room, in silence, since his mother's death.

Muted tells the story of his rehabilitation; a cross between Tommy and My Fair Lady – only much, much, much more down in the mouth than that. With his impatient uncle acting as his guardian, Michael's ex Lauren stops by to see if she can't get him speaking. Her visits are frustrating: for Michael, his lips sealed shut; for Lauren, feelings returning; and for her jealous new boyfriend Jake, Michael's old bandmate.

Michael's muteness is posed as a puzzle, and flashbacks slowly put the pieces together. His mother (Helen Hobson), wine glass always in hand, rails against his chosen career and his choice of girlfriend. Her death hits him hard, but, like Michael, the truth has been hushed up.

Muted aims to dial down musical theatre. It wants to rein in the art-form's tits-and-teeth tendencies for something else; something truthful and heartfelt. Tim Prottey-Jones and Tori Allen-Martin give us a low-key pop score: mellow and moody. Forget variety, here's integrity. Forget wit, here's feeling. It ends up a mope of a musical: a dreay, downbeat pity party set to glum minor songs. It wallows. It whines. It drones on and on.

Musically, it's monotonous. The sound is pure X Factor – all synth pop and falsettos, such obvious chords and plodding time signatures – and it seems all the more generic against an indie scene story. Sarah Henley's book goes for broke: Hollyoaks Omnibus stuff. Seriously count the clichés: bickering bandmates and flickering old flames, big breaks and betrayals. Might Michael break his silence? Er, you think?

Staged on a modish black square – a swing over a paddling pool – Jamie Jackson's production owes a lot to its lighting design. Three soft strip-lit neons glow at the back of the stage and Zoe Spurr's back lighting picks out the actors outlines, lending Muted the sleek, Shoreditch vibes of an xx album cover. It's much more pleasing on the eye than the ear, but it's so superficial: storyline, score and staging all.

Henley strains for significance. As band names go, LostBoy sets out its stall and Michael's a missing person in a left-behind generation. Having fronted an indie outfit – all go-getting enterprise and original creativity – he's left voiceless and broken. "This country's fucked," is his uncle's assessment. He ups sticks for Singapore and its emerging market, leaving the kids to fend for themselves.

Allen-Martin gives a tender performance as Lauren, and David Leopold's Michael maintains a brooding presence in silence, but Henley's script does the actors no favours, robbing characters of reality. That's no way to handle mental health. It looks like a good plot point, not a subject to be treated with care.

Muted runs at the Bunker Theatre until 7 January.

Watch our video in rehearsals with the cast of Muted