What you'd have for you "final meal" has become a pithy personality shorthand in modern culture. So the fact that Simon — a middle-class English boy about to face the firing squad in an unspecified Asian country — opts for baked beans on toast, to the quiet disgust of his respectable, linen-suited father, can be seen as a microcosm for this new play. The fact that Simon soon loses his temper and slams that final meal against the prison cell walls is also indicative of how Ticking wastes its potential with an excess of cynicism.

This is the debut play of filmmaker Paul Andrew Williams, who's enjoyed success with The Eichmann Show on TV, and the films Song for Marion and London to Brighton. He also directs his small but impressive cast here, with Tom Hughes giving a twitchy, volatile performances as Simon, Anthony Head (still best known as Giles from Buffy the Vampire Slayer) as his emotional distant father, and Niamh Cusack as his stricken mother.

Simon's parents have one hour with him while waiting to hear if he'll get a reprieve; he's been charged with murdering a prostitute, but has always claimed his innocence. But how do you spend your final moments together if you've never really felt like a happy family? That's the central question of Williams's play, but his answer never quite convinces. Although uncovering dark family secrets is obviously more dramatic than hugs-all-round, one can never shake the feeling that no-one would be this cruel, or childishly point-scoring, when faced with imminent death.

Simon loathes his father, but for a long time this just reads as spoilt rich-kid arrogance, as he plays glib, Oedipal mind-games with his parents. Hughes certainly conveys the sarcastic, entitled air of the posh modern traveller, convinced his uptight Middle England parents only care about what the crowd at the cricket club will think. But Cusack and Head's characters never really seem that bad — terrific actors both, the grief and love for their son reeks off them.

It feels like Williams plays his cards too close to his chest; for too long, the father seems simply misunderstood. Nasty revelations, when they finally arrive, are a justification; more dramatically interesting would have been to allow these to nettle through the play.

The writing veers between cool construction and histrionic outbursts, trips down memory lane spiked with pitched accusations. There are also nice, perceptive details in Williams' writing that make the set-up believable: Simon's near-orgasmic enjoyment of a Twix bar, or the moment when his mother cries into rough prison handtowels, because she's already run out of tissues.

But overall, Ticking feels like an exercise in cynicism. The high-stakes scenario that enables a final brutally honest showdown is also one that would surely allow resentments to melt away into forgiveness.

Ticking runs at Trafalgar Studios till 7 November