Ooh-er missus. Here’s a modern sex comedy in which a trans woman turns up at a straight, rather strained Islington swingers party run by a coy academic and his very available partner. Before long she is testing everyone’s liberal credentials and the liberated ambience, the nub of the male reaction being “No Sex Please, We’re Possibly Transphobic”.

You can’t accuse the author of The Sex Party, Terry Johnson, 66, of opting for a quiet night in, in terms of potential reactions. It’s one risk to make trans lives a central talking-point in a jocular entertainment, but Johnson raises the stakes by making questions about sexual desire, biological identity and ‘gender ideology’ integral to the storyline. The presence of Lucy, the trans outsider, forces the characters, male and female, to reveal their positions, as it were, in terms of physical contact. Their attempts at sensitivity jostling with their own attitudes, assumptions and sense of self. Lucy represents a challenge: “I am a woman, with a penis”.

I can’t imagine many theatres were keen to give such a thrusting provocation a platform, venerated though Johnson is. Bravo to the unfunded, open-minded Menier, then. Whatever the shortcomings of the piece – there’s a smack of contrivance about Lucy’s presence and caricature stalks the four couples – it’s defined by rollicking dialogue, good old-fashioned writerly craft and an implicit faith in theatre as a forum for exploring difficult, even taboo, subjects.

Johnson eases us into things via enjoyable lashings of middle-class inhibition and marital dissatisfaction in the des-res kitchen as things hot up elsewhere (the carry-on happens off-stage). The gags fly thick and fast. “What are your safe words?” Amanda Ryan’s archetypally bling Russian Magdalena (reluctantly hitched to Timothy Hutton’s ageing wealthy American hipster Jeff) is asked. “Don’t Stop!” she drolly responds. With Johnson directing a crack cast, much of the humour lies in minutiae. “How do I look?” asks Will Barton’s oafish Tim, ravaged by time and drugs. “Like a bewildered corpse,” replies Jason Merrells’s recoiling host.

A sobering conversational quality descends, as Pooya Mohseni’s Lucy finds herself the object of discussion and a magnet for barbs, especially from her rival in the glamour stakes, Lisa Dwan’s glinting Gilly, clinging to an unassailable sense of womanhood. But the sheer poise Mohseni (an Iranian American trans actor) brings to the role, all dignity and hard-won wisdom, has its own power and dampens down an incendiary topic without snuffing it out. For all its knowing bouts of crassness, The Sex Party is sensitively handled. A return to form for Johnson, it invites us to think about what we choose, who we choose, and how we arrive at being truly ourselves.