Jus' Like That! Garrick Theatre, London

Those of us who still associate Jerome Flynn principally with his and Robson Green's rendition of "Unchained Melody" – surely one of the most heinous crimes ever committed in pop music – got a huge shock at the first night of Jus' Like That!, John Fisher's new play about Tommy Cooper. Flynn is a revelation.

In this show, which recreates some of Cooper's most dazzling moments on stage, the actor, who spent several seasons in the drab military television series, Soldier, Soldier, reveals hitherto unknown talents for impersonation. He captures to an almost unnerving degree the spirit of the performer who once said that his magic act was "10 per cent skill, 90 per cent cheek".

Flynn, who has clearly spent weeks locked in a room with old Cooper videos, has cracked every aspect of his stage persona, from the distinctive "hur hur hur" laugh, to the inane grin when a magic trick has failed spectacularly, and the little kick of the leg when a routine works well. The ultimate testament to the success of the portrayal is that it feels like a fully rounded character, rather than a caricature.

The mark of Flynn's confidence in this show, which is directed with panache by Simon Callow, is the fact that he is able to play with the audience. Even when he stumbles on a line, the actor is so assured that he turns it into a gag: "I had my nose fixed, but my teeth don't work."

He is equally comfortable with the play's physical demands. Even when his hair is matted with sweat towards the end, Flynn easily brings down the back-curtain during a bungled song-and-dance routine. But Jus' Like That! is not all fun and games. The middle third of the piece, in Cooper's dressing-room before the show, provides some insights into what drove the man – primarily, a killer combination of booze, fags and pills. He jokes that if his wife were giving the dog a worming tablet, "I'd want one, too".

However, this part of the show overplays the "tears of a clown" motif. For instance, the section where Cooper recalls how the midwife delivering him had said that he should be cast aside as a weakling appears rather bolted-on. But none of that should detract from what is a bravura one-man show. Jus' Like That! could have been a buttock-clenchingly embarrassing homage. But, like The Play What I Wrote, this show succeeds in bringing to life the mesmerising stage presence of a timeless comic act.

Flynn's finest achievement is to wrest the memory of our greatest comic magician from all those third-rate performers armed with fezes and feeble impressions. Who would have thought that Jerome Flynn would be such a gifted purveyor of unchained comedy?

Booking to 21 June (08708 901 104)