A stage-musical adaptation of the well-nigh flawless 1993 movie? Some have asked what the point of that would be – including Stephen Sondheim, who once toyed with the idea of writing one. Well, this hotly anticipated show at London’s Old Vic, reuniting the team behind the smash-hit Matilda, turns out to be such a tonic that it's a pity you can't get a repeat prescription for it. Danny Rubin, who co-wrote the brilliant script for the movie, has joined forces with composer/lyricist Tim Minchin and director Matthew Warchus on a version that retunes our sense of the black hilarity and emotional depth of the central conceit: a man trapped in a time-loop until he breaks the cycle by becoming a better, less ego-bound person.

Cynical weatherman Phil Connors is despatched to Punxsutawney, Pennsylvania, to report on the annual Groundhog Day celebrations, an assignment he has always disdained. But he finds himself doomed to relive that day, again and again. Given that there’s literally no tomorrow, he is able to behave with reckless abandon, knowing that whatever he does, he will still wake up in bed on 2 February. Is this heaven or hell? It’s a situation that can be exploited for the attempt to cheat his way into the bed of his producer. But it's not exactly calculated to disabuse Phil of his arrogant assumption that he's the only real person in existence. Which has long been his curse.

Matthew Warchus’s production is a miracle of stage-craft and technical coordination. The repetitions and comedy jump-cuts in the film were put together in the editing room. In the theatre, Phil’s world is continually being dismantled and reconstructed by the inhabitants of Punxsutawney themselves as they dash around on the travelators and interlocking revolves. It’s a pleasingly rum way of suggesting the community spirit in this town (all tiny lit-up buildings in Rob Howell’s design and the nightmare of Phil’s essential isolation. Broadway star Andy Karl tackles the demanding central role with fantastic aplomb, totally scotching the idea that Bill Murray is indispensable to this material. He’s hilarious with his jerk-you-can't-help-but-like charm and his devilish rhythmic cunning when negotiating those innumerable repetitions-with-variation. It must be exhausting work but he makes the task of carrying the show look effortless.

Minchin’s score isn't as melodically memorable as Matilda and I'm not sure that it's a good idea to kick off the second act with a ballad from Nancy – a young woman tricked by Phil into a one-night-stand – about being stuck in a role assigned to her by men and wistfully hoping that one day “I will be more than Nancy”. It sounds too nudgingly conscious of the themes in the piece as a whole. But allowing song to give us a glimpse into the inner life of Carlyss Peer's very endearring Rita, Phil's love interest, works much better. Her private thoughts about the cliches of romance (“I'd rather be lonely/And sat on my fanny/Than wait for my Prince to come” she insists ) are in droll counterpoint to his indefatigable succession of revised smarmy gambits.

Phil may think that he’s come to know everything about Rita to whom he is perpetually a new-ish colleague. But the curse of recurrence is at long last lifted when, having achieved the best version of himself, he really sees her for the first time. The couple have a beautiful climactic duet about this (“Seeing You”) as the winter darkness gives way to orange sunlight. All the more uplifting and magical for not being the slightest bit soppy. Minchin has a sure instinct for where the characters should explore their feelings about time in song and a wonderful oddball humour: “There'll be mornings you'll be utterly defeated by your laces”. It’s a moot point at the moment whether the production will transfer to Broadway or the West End first after its short run at the Old Vic. But it's a fairly safe bet that, wherever it travels, this show will go on and on being a hit.

To 17 September; 0844 871 7628