A Midsummer Night's Dream, Lyric Hammersmith

Shakespeare’s plays have proved remarkably resilient to everything that’s been thrown at them down the years, including – in the case of A Midsummer Night’s Dream, with its flowery bowers and fairies – cloying Victorian whimsy. Peter Brook’s white box production in 1970 effectively Tippexed out that option for the late 20th century. In turn, this version by the touring company Filter has put down a marker for the 21st.

Premiered at the Lyric in 2012, and now back there after a long tour, it shows, as never before, how hootingly funny this play can be – and not just in the Mechanicals’ scenes. It’s quite a new experience to come away from Shakespeare with aching sides.

Liberties are taken, of course, not least in the positioning of Peter Quince (Ed Gaughan) as a company manager who introduces the show in the mile-a-minute style of an Irish greyhound race commentary. He is thrilled to announce a mystery guest in the role of Bottom, and hints that this is to be none other than Knight of the Realm Sirrrean McKellen. Ten minutes later, alas, Quince is glumly offering refunds at the box office. Sirrrean is stuck in a lift between floors, and will not be appearing tonight.

A heckler in the stalls offers to help out. It can’t be that hard to read a script, can it? This is the first of many comments on the meta nature of this text. The heckler becomes an “amateur” stand-in for a character playing am dram in a play that's already framed within a play. In this endless hall of mirrors, his gauche sight-reading of Bottom’s part is par for the course.

The fairy realm is summoned very neatly. Puck (a laconic Ferdy Roberts, pictured above) is a burly stagehand in a Shoreditch beard with the power to create an entire Radiophonic Workshop of sound effects using just a penknife and a microphone. Meanwhile, Jonathan Broadbent’s Oberon (pictured below) is a bumbling superhero in Austin Powers specs. He can’t even get his invisibility cloak to work properly, never mind the magic juice – lurid blue stuff squirted suggestively from a squeezy bottle that ends up all over everybody.

And yet this isn’t a mockery of the original, or even a gentle spoof. The proof is in the quality of the verse-speaking and the fabulous live rock music, produced onstage by the Mechanicals, and the way director Sean Holmes keeps Shakespeare’s intentions firmly in view at every turn. Oberon’s “I know a bank …” has all its poetry intact. And in a wonderful undermining of expectation, Bottom’s dying speech as the absurdly got-up Pyramus is genuinely heart-wrenching.

The two warring couples are beautifully cast. I’ve not seen a lankier Helena (Clare Dunne) or a more terrier-like Hermia (Victoria Moseley), and you believe they might inflict real damage on one another. Their men are terrific too, each pulling off one of the evening’s many transformations as they turn into microphone-munching, hip-swivelling love machines. Eat your heart out Barry White.

On the whole, the excess and mayhem is perfectly judged, and though an Xbox-style fight between Lysander and Demetrius seemed to me gratuitous, I grant that it might hit the spot for teenage boys. This is a reading that speaks equally to newcomers and those who already love the play. It may even make them love it more.

• A Midsummer Night’s Dream at the Lyric Hammersmith until 19 March