The Recruiting Officer, Donmar Warehouse, LondonThe Taming of the Shrew, Royal Shakespeare Theatre, Stratford-Upon-AvonA Midsummer Night's Dream, Lyric Hammersmith, London

Two very funny Shakespeares and an 18th-century romp join the wave of comedies rolling across the British stage

The best a fellow can do, says Captain Plume, is concoct for himself "some pleasure amidst the pain". Writing The Recruiting Officer in 1706, George Farquhar had experience of Plume's tough profession. The dramatist had been on the recruiting circuit, trying to induce skint Shropshire lads to join the army – till debts forced him to sell his commission.

However, Josie Rourke's high-profile production – her debut as artistic director of the Donmar – is hardly a slice of grim realism, in spite of a programme note professing otherwise. This is a jovial romp, with conniving wiles played for laughs.

Tobias Menzies's Plume is a wenching rover in scarlet coat and tricorne hat. He cocks an eyebrow as his sexual conquests are reeled off by Mackenzie Crook's Sergeant Kite, his sidekick. These scallywags are playing games with gullible fools and various provincial ladies.

In one scene, Crook disguises himself as a fortune teller, adopting a preposterous Slavic accent and twanging an elasticated beard, while Menzies staggers about like Quasimodo. Mark Gatiss's foppish Captain Brazen flounces in a periwig surely composed of several cocker spaniels. Meanwhile, Nancy Carroll's plucky Sylvia cross-dresses as a soldier boy.

British theatre is currently mad for comedy, and 18th-century larks in particular. Rourke's production is winningly intimate, with a foot-stomping folk band onstage and actors flirting with the front row. Rather than continue her predecessor Michael Grandage's refined house style, Rourke opts for the rough-at-the-edges boisterousness more associated with Shakespeare's Globe.

Up close, some of the costumes look low-budget, and the auditorium's make-over is almost twee, with coloured candles round the balcony and embroidered cushions in the stalls. A few cast members need finessing – Rachael Stirling is formulaically mannered, and not everyone is quite on their lines.

Nonetheless, Gatiss and Crook are terrifically entertaining, having a blast. Carroll is charming, as is the relaxed liberalism of Farquhar's characters generally. There's no hellfire for his Don Juans, though Rourke introduces a poignant note as the band-turned-recruits – now wistfully playing "Over the Hills and Far Away" – exit, perhaps to die in battle.

Pleasure and pain crop up again, entangled with more than a soupçon of sadomasochism in Shakespeare's The Taming of the Shrew, rumbustiously staged by Lucy Bailey for the RSC (and now touring). Lisa Dillon is playing dirty as Shakespeare's virago, Kate. First seen in the square outside her father's Padua mansion – the setting being pre-women's lib, circa 1950 – Kate is being punished for unseemliness. With a priest and a pack of chauvinist spivs on her tail, she feigns repentance for a second, then kicks the hell out of them, wrestling with orgasmic panting and ending with a post-grapple cigarette.

Bailey's take on the play is notably physical throughout (with choreography by Liam Steel). David Caves's Petruchio is a strapping lad from the country, not one for niceties. The sexual chemistry is instant, the wooing turned-on and hands-on, with Kate finding herself on the back foot for the first time. There is also wildly funny cameo prancing from John Marquez, Gavin Fowler and Simon Gregor, Petruchio's manservant – half Groucho Marx, half satyr.

Where the production fails is in plumbing any depth in its central scenes, when Petruchio turns tyrant to tame Kate. Yet a clutch of interesting twists are brought out in her final, notoriously cowed speech ("place your hands below your husband's foot"). For sure, Dillon delivers this with a flicker of sardonic scorn, suggesting she's faking meekness. Yet she also looks into Petruchio's eyes with sweet adoration, vulnerable bewilderment, and maybe a touch of the brainwashed groupie. It takes a brave director – and probably a woman – to explore these non-feminist angles.

Bailey adds further layers, not only including the usually-axed prologue but also subsequently keeping the drunken tinker Christopher Sly (who imagines he's a lord) lolling on the edge of the stage – which is, in fact, a gigantic bed. He watches the taming of the shrew as if it might all be his frustrated fantasy.

The real de-light of the week is a quite brilliant, wittily experimental A Midsummer Night's Dream by the youthful troupe Filter (inset), directed by Sean Holmes. It's set in a scruffy basement nightclub, littered with microphones and with a deceptively geeky resident rock band – Peter Quince and the Mechanicals.

Ducking in and out of Shakespeare's script, Ed Gaughan's Quince rabbits like a flailing comedy compère. A tattooed stage manager stomps on stage, tests a mike, and suddenly the place is full off invisible fairies, whizzing like electronic arrows in surround-sound. The SM (Ferdy Roberts) is, in fact, Puck, swigging lager and catching a burbling, Liverpudlian micro-sprite on his fingertip.

What's startling is how Filter manage to be at once tongue-in-cheek and magical, rocking and insightful. Puck's mind-addling love potion – jets of blue ink sprayed from an aerosol can – look like an act of violence and a punky thrill, as the sweetheart-swapping lovers invest Shakespeare's verse with lust and get down on the dance floor.

'The Recruiting Officer' (0844 871 7624) to 14 Apr; 'The Taming of the Shrew' (0844 800 1110) touring to 31 Mar; 'A Midsummer Night's Dream' (0871 221 1722) 17 Mar

Next Week:

Kate Bassett sizes up the latest Essex epic, David Eldridge's play In Basildon

Theatre Choice

Absent Friends, Alan Ayckbourn's 1970s portrait of jaded marriages and lost dreams, proves poignant and comical at London's Harold Pinter Theatre, above (to 14 Apr). Or catch the RSC's exuberantly funny family musical, Matilda – adapted from Roald Dahl, with songs by Tim Minchin – at the Cambridge Theatre, London (to 21 Oct).