Step into Room 35 upstairs at the British Museum right now and you step into the extraordinary world of Grayson Perry RA, Turner Prize winner in 2003, and now the curator of what is almost certainly the most unusual exhibition the British Museum has ever put on.

In Grayson Perry: The Tomb of the Unknown Craftsman the celebrity contemporary potter pays homage to the countless mostly un-named male and female artisans whose work over the ages has made its way into the collections of the British Museum.

It’s also, Perry says, a “journey through my own mind”. A very personal selection, Perry, who conceived the exhibition, juxtaposes 30 of his own artworks — pots, tapestries, sculptures, many new, from his own ‘civilisation’ he calls it — with 190 artefacts from the great ancient civilisations of the world. Among his themes are craftsmanship and sacred journeys, shamanism, relics, ‘magick’, sexuality and gender, and contemporary culture.

Since this is Perry’s world, we meet Alan Measles, the 50-year-old teddy bear described as “the benign dictator of my childhood imaginary world”. Not long ago the bear went with Perry on a pilgrimage to Germany on the gaudy Harley-Davidson outside, and now he pops up in various guises throughout this surprising, satirical, quirky, intriguing, enchanting show.

Grayson Perry is famous for his glazed ceramic pots. The first pot here is You Are Here (2011). As ever, it is covered in witty comments on modern life. But this is especially for exhibition-goers, and here we are with speech bubbles saying: “There was such a buzz about it on Twitter,” a twenty-something; “I try to keep up with what’s going on in the arts,” an older woman in a chunky knit.

“Do not look too hard for meaning here,” warns Perry. “I am not a historian, I am an artist.”

This is probably wise. No sequel to A History of the World in 100 Objects, last year’s radio success for the British Museum, this is not so much about the objects, it’s more about Perry himself, and the juxtapositions: the links and likenesses felt intuitively by Perry and rationalised in the displays.

Statements everywhere: The Rosetta Vase (above) about getting to understand other cultures; The Frivolous Now (2011), a wry take on modern life, covered in buzzwords: OMG, Facebook, Big Society, Botox, Product Launch, Celebrity Gossip. Evidently, Perry is none too impressed with the 21st century.

Everything in the British Museum was contemporary once, the displays remind us. Some displays are so fine-tuned it’s hard to tell historical and modern objects apart — which may make viewers look again at the museum objects.

Tibetan amulets alongside Perry’s ponytail, 20th-century photographs of Japanese drag kings and queens opposite transvestite Perry’s fancy Japanese cape, an amazing Malian Boli figure, a giant ox, like a prehistoric wall painting realised in mud and clay, 17th-century Staffordshire plates. It’s weird and wonderful, this show — it’s even one the museum averse might warm to.

The show can be seen until February 19, 2012.