Appropriately for a play that begins with a shipwreck, Simon Godwin’s Twelfth Night at the National Theatre left me with a lingering sinking feeling. The production is a watershed (I’ll stop) in cross-gendered casting, with Tamsin Greig’s Malvolia creating a mannequined Miss Hardbroom that kicks over the traces of Sir Donald Sinden, Richard Briers, Sir Nigel Hawthorne, et al. Less prominently, Doon Mackichnan plays Feste as a principal boy-turned-raver, and Imogen Doel carries equal opportunities to its logical conclusion by having to make the best of Fabia[n] – which she does very well, despite dialogue like ‘Sowter will cry upon’t for all this, though it be as rank as a fox’, a line so bad it merits mention in The Art of Coarse Acting. My problem is that this production, lauded for its celebration of race, sex, and gender, inadvertently uses cross-casting to tell a deeply homophobic story.

On the surface, there’s much to like. Soutra Gilmour’s inventive set unfolds from a ship into an endlessly rotating pyramid that’s somewhere between Illuminati shout-out and a tomb by Canova. There’s a jacuzzi in which Phoebe Fox’s Olivia becomes a floozy (mourning garb replaced by a red bathing suit), any number of zooming cars and motorbikes, and a salmon-pink fountain that delights the audience by spurting symbolic jets on cue. The costumes are similarly witty, with Mackichnan’s Feste flaunting a sea-green tribute to Princess Beatrice’s pretzel-themed millinery.

There are also some excellent performances. Excluding Greig, chief of these is Daniel Rigby’s pink-suited Andrew Aguecheek, who, as Bertie Wooster with a manbun and an energetic vogue for disco, overshadows Tim McMullan’s Sir Toby, a rat-bitten roué.

Oliver Chris’s Orsino is the first truly loveable one I have seen, a superhero Prince Charming whose spoilt temper is sublimated into boxing, and who takes the audience into his confidence with winning ingenuity. He tussles readily with Tamara Lawrence’s Viola, an unusually even-tempered, cheerful heroine whose tendency to take all the verse at full pelt robs her bittersweet dialogues with Orsino of all their self-concealing pathos. She calls her situation a ‘barful strife’ but laughs her way through the first two acts, until the joy of being mistaken for a still-living Sebastian (‘Prove true, imagination, O, prove true’) yields the first moment of emotional connection.

This is a production where love electrifies and mobilises: Olivia gyrates to the onstage musicians’ elevator music, while Viola wriggles and hoots after Orsino gives her a kiss to deliver to Olivia. Ultimately, these are twins whose highest priority will always be each other; Daniel Ezra’s pugnacious, sexually opportunistic Sebastian (an excellent performance) seems bemused by both Antonio and Olivia’s devotion, but adores his sister.

And then there’s Greig’s Malvolia. Every time she takes centre-stage, she brings with a consummate skill in verse-speaking that is sometimes absent elsewhere. Godwin’s production seems uneasy about the text: switching pronouns and honorifics in line with gender leaves characters ‘lady’-ing each other in the manner of vintage Coronation Street, but more important is the overriding feeling that the text is an impediment to the evening; a struggle to be overcome. One oddity is that Lawrance plays Viola with a London accent, while Ezra sounds West African; while they can’t be visually or acoustically identical given their biological sex, giving them such different accents is a baffling test of audience credulity.  Monologues are largely galloped through, Belch supplies ad-libs (Maria is a ‘dirty little girl’) but loses lines that illuminate, including Olivia’s revealing reluctance to ‘match above her degree’ by marrying the count Orsino. This is key to the psyche of the only Shakespearean heroine who uses her last line to insist she pays for her own wedding. Greig gives an electrifying performance, beginning as an obsessive-compulsive spinster, all angular bob, geometric gestures and gym shoes.

Every sympathetic Malvolio incurs tragedy when his passion is mocked; Greig intensifies this, partly by being pitched against an unusually unlikeable gang of ruffian sots, and partly through her bewitching incredulity when she believes her love for Olivia is returned. Her cross-gartered yellow stockings are tights with a pierrot jacket, the latter removed to reveal a primrose bodice and hot pants. Blindfolded and bound, her bare skin increases her vulnerability, and the denouement completes her humiliation – worse than her imprisonment is the realisation that her employer does not, after all, share her feelings – something this single-minded Olivia reveals with remarkably little sympathy.

Greig is an accomplished comedian, whose wit and timing provide all the necessary laughs before the swoop to tragedy: she is an hilarious and heartbreaking Malvolio, and this Olivier production a worthy forum for her talents. Simply making Malvolio’s desire for Olivia same-sex does not necessarily make Twelfth Night a homophobic production, or even a more homophobic play: poor old Antonio must necessarily watch his beloved pair off with Olivia. And there are some genuinely gender-queer moments of light-hearted comedy – Orsino, on his last lines, accidentally snogs a cheerfully acquiescent Sebastian.

The wider tone disturbed me. Antonio is probably textually gay; this Malvolia pines for her mistress. But Twelfth Night stages a third great losers in love: Antonio, Malvolio, and Sir Andrew – and in Godwin’s production, Sir Andrew is also queer-coded, from his pink clothes and long, frizzy hair to his penchant for cuddling up to both Sir Toby (much to the latter’s disgust) and to the teddy bear Orsino gives Olivia. This is troubling not because it queers a Shakespearean icon, but because it does so via unimaginative stereotypes, as if Agucheek’s incompetent flirting and cowardly duelling mean only one thing. Rigby is an accomplished comic, but the net result is a production with three queer characters, who are also the three to end up humiliated and alone.

Also disconcerting is Orsino’s suddenly-averted gay panic when Viola turns out to be a girl, not a boy: a common moment in productions, but especially jarring when Oliver Chris’s Orsino had shown so little sign of desire for his page. In a production more sensitive to queer identity, the denouement might feel more ambivalent, but clichés abound. The Elephant (an Illyrian tavern, and Antonio’s intended lovenest) appears as a gay nightclub, in which understudies for The Village People hear a black drag queen perform Hamlet’s ‘To be or not to be’ speech as a torch song. This showcases Emmanuel Kojo’s considerable singing talent, and provides an enchantingly funny moment when Rigby’s Aguecheek instantly corrects his ‘Now, sir’ to an ad-libbed ‘Sorry, miss’. But the interposition of another play’s text only reiterates this production’s discomfort with its own, and the gratuitous, glamorous drag queen affects an inclusivity the production doesn’t really possess. Elsewhere, the straight characters’ homophobia is largely played for laughs, and despite Greig’s brilliant, innovative performance, this ‘genderfluid’ Twelfth Night ends up feeling straighter than ever.

 Twelfth Night will be broadcast live as part of NTLive on 6 April. For more information, including the programme of education events, see the National Theatre website.