Although it dominates our lives, Brexit has so far made surprisingly few appearances on stage. It is, however, a key topic – along with grief and cycling – in this humane, funny and perceptive two-hander written by John Godber and performed by him and his wife, Jane Thornton. This is certainly the first play I’ve seen that seeks to explain why so many people voted leave.

It presents us with an odd couple brought together by loss and a love of bikes. Don, an ex-miner and now a porter at Pontefract hospital, is grieving over the death of his wife. Carol, a teacher and would-be artist, is a widow haunted by the passing of her architect husband. But, after a chance graveside encounter, the two of them discover they have a shared passion for cycling. Rashly they set off on a bike-and-train trip to Florence on the day of the 2016 referendum, only to realise that they are on opposite sides of the argument about Europe.

Godber has a gift for evoking a whole world through a single line, as when the celibate Don gloomily remarks “a mate set me up with a date in a curry house in Scarborough”. There is also much funny business with collapsible tents when the stranded pair are forced to spend a night together under canvas. But the heart of the play lies in Don’s explanation of his decision to vote leave, which dates back to the scars left by the miners’ strike of 1984 and which is fuelled by his daily confrontation with deprivation and poverty. Carol counters by pointing out the illogicality of Don’s description of politicians as “bloody clowns” and belief in their promise to divert savings on Europe to the NHS.

The irony, however, is that the couple are mutually dependent since they are crossing the continent on a tandem.

Godber and Thornton not only pedal furiously on a stationary bike (a Brexit metaphor?) but also impeccably suggest a couple divided by class and outlook but united by loneliness. Even if you doubt whether they would ever get together again, the play pins down many of the motives of the leavers and makes you laugh out loud. It is salutary to hear, only a few hundred yards from the palace of Westminster, the place bitterly dismissed as “just a finishing school for Celebrity Big Brother”.

• At Trafalgar Studios, London, until 27 April.