They dance, sing, quarrel and fight like real troupers, do Tom Chambers and Laura Rogers as Elyot and Amanda in Noël Coward's brilliant 1930 comedy of lust and loathing in the South of France and Paris.

This perfectly structured quadrille for two newly married, inter-related couples on honeymoon kicks off when Elyot, hooked up to Sybil (Charlotte Ritchie), eleven years his junior, discovers old flame/ex-spouse Amanda with her boring new beau Victor (Richard Teverson) on an adjacent hotel balcony. They elope adulterously and renew their amorous hostilities.

Tom Attenborough's efficient production runs the first two acts together, which is asking a lot of the over-stretched leads, who maintain Coward's rhythm and brittle dynamism without really taking flight; two intervals would undoubtedly help, and honour the play.

But we do at least understand perfectly that this is all as much about trivial irritation at close quarters in a relationship as it is about jealousy and possession. Amanda and Elyot love each other very much, but also don't like what they love, often the best and liveliest sort of love: they are like "two violent acids bubbling about in a nasty little matrimonial bottle."

The Bromley auditorium is a tough one for this sharp, rapid dialogue with stiletto jibes and effervescent exchanges – the show tours next week to stops including Stoke, Brighton, Birmingham and Glasgow – but Chambers' Elyot, despite a thin, inflexible voice, makes the most of the hits and fizzes. Rogers' Amanda, arrantly bohemian and gorgeously athletic in silks and bare feet, is a close second to Anna Chancellor's recent full-on free-spirited luxuriancein Chichester and the West End.

Lucy Osborne's touring set is okay, a little flimsy on the balconies, a little too drab and functional for the Paris apartment, though there's a hilarious flying entrance from Victoria Rigby as the maid discovering the mayhem of the morning after. Love songs, moonlight, the potency of cheap music: these run as secondary counterpoint to the harsh, hilarious realities of suspicion and bitchiness.

Did that girlfriend in South Africa have a ring through her nose? (One of the few lines the Coward estate might be advised to expunge were it not necessary for the rhythm of the inevitable riposte – "Don't be revolting"). And there's something bracingly shocking about the fact that Amanda and Elyot have been in love for eight years: three of them married, five, divorced.

Celibacy was not a serious option for either in the latter five, so they are even more interested to know what might or might not have happened in between. This is so funny, and so true, that the play becomes that absolute rarity, a genuinely contemporary period piece. And of course its wit, brilliance and satirical sheen remain undimmed, even in Bromley.

Private Lives runs at Churchill Theatre, Bromley until January 23 and then tours the UK.