Last week, the playwright Samuel Adamson tweeted an image of the cast list from his 1999 adaptation of Chekhov’s Three Sisters. It was one of those propitious line-ups where nearly everyone went on to become a success on screen or stage: tucked at the bottom, in the role of the sub-lieutenant Fedotik, was Michael Fassbender. But what was most impressive was the women: Kelly Reilly, Indira Varma, Chimerica’s Claudie Blakley and the BAFTA-nominated TV actress Claire Rushbrook. Judging from the electric performances of its cast, especially its women, Swings and Roundabouts at Kennington’s White Bear Theatre may well prove to be one of those productions.

Swings and Roundabouts is a loose adaptation of Arthur Schnitzler’s classic La Ronde – the merry-go-round of sexual encounters that scandalised 1920s Vienna. Its daisy-chain structure, in which each character has a liaison with the next, has been so ceaselessly mined – most recently in Florence Keith-Roach’s disco-inspired Love To Love To Love You at St Martin’s Lane at The Library – that any adaptation bears the burden of finding a fresh angle. This could be in the staging (such as David Hare’s The Blue Room, which reinvented the format with just two actors), the sexual orientation (Peter Scott-Presland’s 2011 version at the Rosemary Branch Theatre, which was set in a gay bar) or the time period (the Harbinger Company’s 1950s-set version in 2011, also at White Bear). Swings and Roundabouts shrugs off these concerns. It makes no grand social statements, nor does it play fast and loose with the staging. Instead, its theatrical conceit is so obvious that it’s inspired: that it is, in the best sense of the term, an actor’s play.

Indeed, it comes as no surprise that the writer/director of Swings and Roundabouts, Richard Listor, is himself an actor; he also stars in the show as the Executive Producer, the equivalent of Schnitzler’s The Count. The role is an understated one: as in the original Schnitzler, he is outshone by the irrepressible force of nature of The Actress, a wild grenade of sexual charisma played with vital exuberance by Greek actress Anna Danezi. This is a microcosm of the production, which – arguably like La Ronde itself – belongs, ultimately, to the women; the play’s assembly of dynamic actresses from across Europe makes a persuasive case for a ‘Yes’ vote in an EU referendum. In addition to Danezi, Poland’s Aggy Kuk as ‘The Sweet Young Thing’ – a 19-year-old who poses for an artist after an uneasy encounter with a philandering husband – swings impressively between guarded reserve and youthful excitement. Meanwhile France’s Margaux Billard, as ‘The Prostitute’ who bookends the play, combines a world-weary vulnerability with the glittering magnetism of a future star.

Although the programme makes some reference to sex and modern society, there are some questions about whether Swings and Roundabouts passes the “why now?” test. But ultimately it doesn’t matter. It has a swagger and theatrical energy that eclipses chronology and, much like the White Bear’s Women of Twilight last year, it is its female performances that make it so irresistibly alive.

Swings and Roundabouts played at the White Bear Theatre.