First Night: The Comedy of Errors, Olivier, National Theatre, London

After One Man, Two Guvnors, the National Theatre now gives us "One Play, Two Sets of Identical Twins", aka, The Comedy of Errors, another play that is – in part, at any rate – a rumbustious romp. The face that dominates the poster for Dominic Cooke's almost excessively inventive modern-dress production is that of Lenny Henry, who is virtually a Shakespeare veteran now after his extraordinarily brave dive into the deep end with Othello.

He's the big box-office draw here and he's wonderfully funny. What's admirable, though, is that there's no suspicion that the play has been twisted into a star vehicle for him; he's part of a fine ensemble that work hard to animate an over-cluttered concept and eventually drive the proceedings to a pleasing crescendo of comic mayhem.

In this early play, Shakespeare frames a virtuoso farce of mistaken identities within a narrative that prefigures the shipwrecks, sunderings and miraculous reunions of the late romances. What underpins both aspects is a sense of that search for one's other self without whom any person feels psychologically and emotionally incomplete.

I'm not sure that Cooke best prepares for this link by presenting the back story as a detailed re-enactment, replete with whirling helicopter rescue services, which erupts all over Bunny Christie's extraordinary, three-tier set.

With a strong Nigerian accent and cultural supersititions, Henry plays Antipholus of Syracuse, who lands in Ephesus in quest of his long-lost twin and with his servant Dromio (adorable Lucian Msamati) in tow. Ephesus in the original is a place associated with witchcraft and sorcery. Here it's like a dodgier version of present-day London and in the new-look opening, aptly for a play about unstable identity, we see the elderly Egeon (an impressive Joseph Mydell) mugged and robbed of his passport as well as condemned to death.

Henry beautifully conveys the tragicomic plight of an innocent abroad. It's typical that in this production his character declares "There's not a man but doth salute me/As if I were a well-acquainted friend", while absently nudging aside a six-foot-five transsexual in PVC miniskirt in the red-light district.

When a woman claiming to be his wife (the ever-excellent Claudie Blakely as a shrewd as well as shrewish Essex fashionista) crosses a billiard table on teetering six inch heels to remonstrate by clutching his gusset, Henry becomes an hilariously still statue of eye-rolling bafflement. He's great at the physical slapstick, but he also gives real emotional depth to the role, particularly in the scene of dignified, dawning love with his twin's sister-in-law (Michelle Terry) through whom he yearns to re-establish a sense of self.

In the final act, a production needs to show how the frantic incredulity provoked by farce shifts to the calm wonder stirred by romance. That doesn't quite happen here in a staging where the Abbess who officiates over the reunions becomes a therapist in the Abbey Clinic. Lurching from penthouses to knocking shops to Harley Street, this Comedy of Errors ends up sacrificing poetry to ingenious prose.

This production will be broadcast, as part of the NT Live season, on 1 March 2012