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This epistolary story of two people looking for love is the ultimate antithesis to the modern-day dating app. Set in a time when a message was less a flighty ping away, more as slow as the postal service, it is a delightful romcom through letters. It features Jack (Preston Nyman) and Louise (Eva Feiler), who begin writing to each other because family members think they might make a match. It is 1942, Jack is a military doctor tending to burns and amputations while Louise is a dancer trying to break into Broadway musicals.

It goes from stiff opening courtship to a chalk-and-cheese meeting of minds and then develops into a genuine relationship, all without either having met, the first date forever being deferred because Jack can’t get leave, or Louise is in a touring show.

Written in 2019 by Ken Ludwig, a well-respected figure on Broadway (he wrote the book for the musical Crazy For You, among other achievements), there is not the same “will-they-won’t-they” dramatic tension if you already know that the story is based on that of Ludwig’s parents. Yet he makes you rally for this couple, even in spite of characters who seem familiar, speaking in broad tones to a wartime soundtrack of all the golden oldies. Ludwig elevates it all from beyond its cliches.

Directed by Simon Reade, the production’s strength also lies in its simplicity: two actors giving remarkably honest performances on opposite sides of the stage. You feel an incorrigible warmth for them as they try to snatch happiness in a time of war.

It is sweet, funny and surprisingly moving, even as it leans into its nostalgic weepie spirit. Alongside its increasingly ardent love story, it contains the romance of letters – the ink-and-paper intimacy of them, the having to wait and the physical touch.

A twist towards the end tries too hard to add emotional jeopardy that is not needed. You are already feeling for this pair, willing the war to end so they can be together. Yes, it’s an idea as well-worn as Vera Lynn’s We’ll Meet Again, but an irresistible heart-warmer too.

• At the Arcola theatre, London, until 2 May