Laura Wade is the scourge of the Bullingdon Club, apparently. Her play Posh – and the film that followed it, The Riot Club – has so besmirched the Buller's reputation that, these days, no self-respecting Old Etonian would be seen dead in a mustard waistcoast. Far from a move that makes you for life, it's become a form of career suicide.

Having premiered precisely as two former members, Messrs Cameron and Osborne, moved into Downing Street, Posh landed as a withering satire on the upper echelons of establishment power. It showed a fictional Oxford student dining society – definitely not the Bullingdon for very good legal reasons – returning to life as a host of silver-spooned students drink themselves near-blind, gorge themselves near-stupid and wreak havoc on a small country pub. It became a big hit: as much a blast of boys-behaving-really-really-really-badly as a staged Punch cartoon.

Posh is very much an all-male affair, so an all-female production is an intriguing idea, but it's one that director Cressida Carré rather lets slide. Her Riot Clubbers appear in cravats and tails with big, salon-fresh hairstyles. It's not drag exactly, they're not playing men, but it is a kind of male impersonation. They slouch. They manspread. They pump their groins. Like Melissa McCarthy's take on Sean Spicer, the mode is a means of lampooning. The trouble is Wade's script lampoons in itself. Doubling up does it no favours.

Otherwise, to borrow a phrase, this is about women getting their mitts on some choice male parts – and fair enough. Just as the History Boys did alright for themselves, a lot of the Posh lads have got good things going. Why shouldn't young women get the same sort of launch pads early on in their careers? It's all sorts of galling that, for all their brio and brilliance, none of the Ladies of Perpetual Succour have been snapped up for stardom as yet.

There's meat in the gesture. Posh is a play about privilege, so cross-gender casting – even just for the simple opportunity of it – does its bit to overturn that. It's a smash-and-grab job, essentially. Take the plum roles and run. The problem is that Cressida Carré's approach never fully lets women really own that. In fact, it positively works against them.

Playing the parts much as men might, it becomes a case of anything you can do, we can do just as well, thankyouverymuch. Only not like this they can't; not like for like. It's painfully obvious that none of them have stepped inside a room without women, let alone a male psyche. Inevitably, the whole thing's a tad off; the joshing, the jinks, the powerplay. It just smells wrong. The rhythm's off. The details are out. These aren't male insecurities, urges or egos, but approximations of them. Everything's played from outside. Every character's judged and, so, the drama deflates.

Wade's play was always a pretty blunt instrument, and it needs flint-sharp performances to sustain itself. With the Buller Boys out of power, it's lost some of its political sting too and, while Carré makes a case for fresh topicality with Theresa May in the top job, it's a hard sell.

Instead, the charred black walls of Sara Perks design suggest that the damage has already been done. The aesthetic is of devils dining at hell's kitchen as a candleabra swings overhead. Between scenes, the Rioteers spin through slow-mo, strobe-lit bacchanals to raucous punk classics. For all their fineries, these are the real yobs. They have smashed more shit than any anarchist ever could. The tone, at times, is almost mournful.

That said, Wade's play has its own exuberance and, even off-the-boil, it's enjoyable for all its excess. What's missing here is the ugliness, the danger, the threat – all the stuff that really sticks in the craw. Serena Jennings can't find the vitriol underneath the Riot Club's ringleader, Alistair Ryle – the snarl that slowly bares its teeth – and neither Amani Zardoe nor Cassie Bradley muster the cutthroat rivalry of two proud, entitled shitbags outspending one another. Molly Hanson gives sanctimonious swagger to Toby "Tubes" Maitland that unravels in drink, and Alice Brittain leans back and looks down at the world as golden boy Harry, but mostly, more gets lost than gained.

True, the casting highlights the ‘ladsladslads' chauvinism at the table, and the boasts of "pussy" and blow-jobs all seem rather pathetic – but then they always did. Indeed, it changes less than you'd think. Smashing the joint to pieces still seems more affronting than crass attempts at sexual assault. It probably shouldn't.

Posh runs at the Pleasance until 22 April.