The British Museum’s press officer, Claire Coveney, comes hurrying up to take me to the galleries of the museum’s latest hot-ticket show, “Shunga: Sex and pleasure in Japanese Art,” and I’m not surprised she looks run off her feet. Pre-opening interest in this new exhibition — the most comprehensive ever assembled of Japan’s explicit and enchanting “Spring pictures” (shunga) — has reached fever-pitch in the press. Britain’s usually well-behaved gallery-goers are, quite frankly, gagging for it.

“I keep getting calls from editors asking for more non-explicit pictures to go with the articles or stories,” says Coveney. “I have to say: ‘There really aren’t any, sorry!’ “

That’s because this show celebrates shunga in all its outsize and unexpurgated glory. Those under the age of 16 may enter only with an adult. And yet beyond all the headlines — a museum famous for its “blockbuster” exhibitions has finally served up a “bonkbuster” — this is a superbly interesting, academically groundbreaking, and oddly touching display of one of the world’s most infamous artistic genres. Appropriately enough, it is a coming together of four partners: the British Museum and the University of London’s School of Oriental and African Studies, with the Nichibunkan (International Research Center for Japanese Studies) and the Art Research Center of Ritsumeikan University in Kyoto.

“One thing we wanted to do, that feels new,” says Timothy Clark, curator of the British Museum’s Japan Galleries and co-curator of the exhibition, who gives me a tour shortly before it opens, “was to explore the medieval origins of shunga, just as at the end we (also) look at what happened to shunga in the modern world, the age of the camera.”

One striking early work included is ‘The Book of Acolytes,” known to date from 1321 but with even earlier, 11th-century, origins. It’s represented here by a 19th-century copy, as the original is locked up in Sanboin, Daigo-ji Temple, Kyoto. The reason for that may be its subject matter: the sometimes tender, often licentious sexual relations between young acolytes and older monks. It makes the smutty tales of monastic indiscretion popular in medieval Europe, told by writers from Chaucer to Boccaccio, seem positively innocent.

Clark pauses in front of one curious 17th-century handscroll and points out that its shaven-headed protagonist is no monk, but a Buddhist nun. In a sequence of scenes, the nun eagerly impales herself on a phallus extruding from what looks like an outsize Christmas present. Finally, the gorgeously-wrapped package bursts open to reveal a lusty naked man. This work revels in the title “Priest in the Bag,” one of several versions of a tale whose female characters have as good a time as the titular monk. It’s impossible to look at it and not smile.

Indeed, this show exudes delight and amusement — it was with good reason that one early alternative term for shunga was warai-e, or “laughing pictures.” But there are dark corners, too. One case holds a creepy selection depicting sex with monsters and supernatural creatures, while Clark glides past another murmuring that it contains “the notorious octopus.”

Yes, that’s the octopus — probably the most famous work of shunga known outside Japan, depicting a pearl-diving girl in coitus with cephalopods. Not all of its foreign fans, though, know that it is the handiwork of Katsushika Hokusai, who can equally lay claim to creating the most famous Japanese artwork known outside Japan — his woodblock print “The Great Wave off Kanagawa” (1829-32)

This may be the most surprising insight the visitor with little prior knowledge of shunga takes away with them — that many of these erotic prints came from the hands of the Japanese artists most celebrated today. The case for the artistic potential of shunga is triumphantly made in a display of works by Hokusai, Utagawa Kunisada and, above all, Kitagawa Utamaro. A woman’s foot, curling in ecstasy, is caught in a mirror in one scene by Utamaro; Clark declares it his “favorite detail in the whole exhibition.” Shunga was not marginalized, and definitely not demonized, as pornography is today.

Then it’s off on a journey through yet more permutations of shunga: its uneasy relationship with the formal “floating world” of sex-work, (“In the floating world, the approach was nothing at all like shunga,” says Clark. “It was all about making the client wait, over many visits, for that eventual sexual encounter”).

There is shunga with a whiff of politics, depicting courtiers and intimates of the Imperial palace, which likely sparked a still-mysterious crisis in 1722 that led to moral reforms and a 20-year-long cessation of the production of shunga. There are cock-spotting guides to the stars of the stage, where famous kabuki actors are depicted full-face accompanied by a detailed genital close-up. There are subversive pornographic satires of Confucian good-conduct manuals, wooden votive phalluses; a case of exquisite tortoiseshell and ebony sex toys. It’s all weirdly, gloriously, life-affirming.

And then there’s a final room, smaller and more dimly lit than the others. This charts the advent of modernity and the intrusion of the gaze — and the morals — of the outside world. It was a shock to the Japanese, who at first proudly displayed albums of shunga to foreign dignitaries in the early years of the country’s opening to the West in the mid-19th century, to realize that their artworks were deemed revolting and obscene. Ironically, Western artists, such as Pablo Picasso, John Singer Sergeant and Toulouse Lautrec came to be secret shunga collectors, and to varying degrees the influence of shunga can be seen in their output.

But along one wall are some early “erotic” photographs from Japan, taken by both Japanese and Western photographers. In two prints made circa 1877, a man and woman make love in a tableau in which the furnishings, clothing and poses closely resemble those of shunga. But while the woman looks vacantly into the camera, the man turns away, hiding his face. Perhaps he’s ashamed to be participating, or perhaps it’s simply so a male viewer can more easily imagine himself in his place. But in shunga, no one turns away from their partner.

In this one image, an entire playful, artistic, passionate genre shrinks down to drab modern pornography. It’s unexpectedly and powerfully sad.

“Shunga: Sex and pleasure in Japanese Art” runs till Jan. 4, 2014 at the British Museum, Great Russell St., London; admission £7 (no unaccompanied under-16s). For more details see www.britishmuseum.org/shunga. It is hoped that a version of the exhibition will travel to Japan, but no details are yet confirmed.