Paradise means – to the imagination of cold, grey, pinched Western Europe – sun, sand, palm trees, clear blue skies. And that’s what floats ethereally around the heads of the Englishwomen on the Jamaican beach on which Sugar Mummies is set. Floating through their minds is the idea of the perfect man – loving, caring, young, fit. Floating before their eyes are the men who meet that fantasy.

All that’s needed to turn fantasy to clenching reality is a little cash. It is these transactions, the female sex tourism now understood as standard in certain small parts of the world, that are the subject of Tanika Gupta’s new play at the Royal Court in West London. It seems it is a subject whose time has come – recently covered in the RSC’s excellent Trade, and Charlotte Rampling’s movie Heading South, about 1970s Haiti.

And Gupta could hardly have picked a better topic to produce a flood of free publicity from male-edited newspaper editors wondering what it is their wives get up to “girls’ weeks away”. The Daily Mail was particularly exercised by the fact that the actress playing Maggie (Linda Bellingham), the oldest and most cynical of the women, had been the face of wholesome British motherhood in Oxo adverts.

But beyond the news value, what is the value of the play, and the production?

First the play: a neat structure – too neat. There’s the women: cynical old Maggie, who just wants the sex; the desperate-for-romance-and-children schoolteacher Kitty (Heather Crane); the young innocent Naomi (Vinette Robinson); and the token black American, Yolanda (Adjoa Andoh), who is knowing and wise to the ways of this world. Her compatriot among the males (and her partner) is Reefie (Victor Romero Evans), who arranges “jobs” for the youngsters on the beach. The young innocent desperate to join the game is Antonio (Jason Frederick); the old hand Andre (who perfectly meets Kitty’s fantasies); Andre (Marcel McCalla) the man standing self-righteously aside from this, nursing his dreams of cooking school. Watching over it all is Angel (Lorna Gayle), Andre’s mother, like a solid mother goddess who has lost most of her powers.

These are far too much sketched/predictable characters – it is only Naomi, whose tale is about the second-generation effects of the trade, but also a very ordinary story of a young woman seeking a parental guide, who emerges with any really humanity. And the obvious balance of the play mean the revelation of the identity of her father is all too obvious long before it formally emerges.

The characters too don’t so much interact as bounce – sometimes all too explicitly – off each other. They seem to always be either grappling or yelling – all points of conflict are dealt with in one of these non-verbal, non-informative, and non-resolutional ways. And some of the women’s behaviour when angry is wholly unbelievable – the overt references to slavery – the whipping, the “unsayable” insults – seem to shoehorn a message – “look, this is almost slavery – a replay of it” – where it simply doesn’t fit.

So that’s the play – what of the production? Well it leaves little to the imagination, and not in a way that provokes good feelings. One scene between Sly and Kitty – involving rapid food consumption and desultory female pleasing – sticks in the mind as particularly wince-inducing.

Robinson’s is the standout performance – she imbues this edgy young woman with a believable flood of innocent desire. Evans too is powerful as Reefie; most of the others are bigger on enthusiasm than subtlety.

There are some fun slapstick scenes early in the play, but black comedy is a tough trick to pull off; it is with the darkening tone that this play, and production, really come a cropper. There is no doubt in the real-life story being told here a mismatch between romantic fantasies and nasty physical and social realities, but to display them in the theatre requires a surer grasp of tone and a subtler portrayal of motivation and desire.

The production continues until September 2. It will then tour to Bolton and Birmingham.

The theatre (with online booking). Other views: Paul Taylor in the Independent; Kate Kellaway in the Observer; a Guardian interview with the playwright; a GMTV interview with Linda Bellingham.