Hussein Chalayan is the godfather of intelligent fashion, his work ranging from high-concept sculptural pieces to utterly wearable frocks. But unless you’re in the front row at Paris Fashion Week, you almost never see it in the flesh. Most of us have to make do with the brilliant, enigmatic short films he directs (Absent Presence with Tilda Swinton was the hit of the 2005 Venice Biennale) and occasional snaps of Madonna in his dresses. Which is why this retrospective is so timely.

Chalayan, 38, a London-based ­Turkish-Cypriot, calls himself a “design artist”. He is fascinated by the interface between fashion and technology, and his work takes in architecture, science, philosophy and anthropology — just listing it makes it sound boring but trust me, it’s not.
He has buried dresses in his garden to decompose, sent models out in dresses operated by remote ­control (mocking our love of authority) and fashioned furniture that turns into clothes.

Designed by architects Block Associates as a series of pods-cum-changing rooms, the Design Museum’s exhibition is given room to breathe and revel in its own sense of fun. Particularly loveable are the original airplane dresses that fold up as airmail envelopes, and mad laser-cut tulle puffballs and morphing underskirts.
You’re torn between ­puzzling just how he gets the LED lights and moving lasers to work, and melting over the little black dresses and silk chiffon shifts.

In one cheeky installation the ­mannequins are actually painting the walls. The Chalayan girl gets to travel, too: in the short film, Place to Passage, a gorgeous Amazon climbs into a pod-like spaceship and, discarding all the painful baggage in her life, literally flies from the streets of London to Istanbul.

For an intellectual designer, Chalayan does not shy from sex. His dresses lift and part, showcasing leg and crotch, but always with exquisite grace (a favourite Chalayan word). This is never objectification. “Anything to do with the body and the female form ­represents power and magic. It’s the ultimate ­symbol,” he claims.

Despite being named Designer of the Year twice, Chalayan has never found it easy making a living (his uncompromising vision has ensured he is less famous than his St Martin’s contemporary, Alexander McQueen). He has gone bankrupt and despaired. But now in his role as creative director of sport ­fashion at Puma, he seems to have hit his stride. His dream client is still Kate Bush: let’s hope she gets to this show.

Until 17 May(020 7403 6933, www.designmuseum.org)