Hokusai’s The Great Wave (also known as Under the Wave off Kanagawa or, simply, The Wave) is one of the most iconic images in art. Today it’s featured on all sorts of merchandise from wine labels and tourist brochures to book covers, gift bags, fans and even underwear. But in 1831, it was the first in a series of prints, Thirty-Six Views of Mt. Fuji, with the towering blue wave only playing a supporting role. The Great Wave appeared in its day as a piece of commercial art, akin to today’s posters—mass-produced for and by the common people. It was “discovered” in the mid-19th century by the European avant-garde, who considered Hokusai’s works to be fine art and compared him to Western artists including Goya and Rembrandt.

As the British Museum presents its first big Hokusai ex...