What it shows is artists’ delight in the new challenges the Near East set them. Here were fresh, unhackneyed subjects for their brushes; the dry, fierce light of the desert and the blue cool of the courtyard, the bright shards of tiles and the patterned folds of cloth. They may have been painting landscapes, but these were of the very places where the prophets and Jesus walked; their street scenes portrayed the fiefdom not of European princes but of the Grand Turk himself; their portraits depicted travellers who had seen things few stolid burghers ever would.

The exhibition is divided into Orientalism’s natural categories — genre, landscape, portraits, the harem and religion. It spans some 300 years, starting with the anonymous but splendidly decorative portraits of Sir Robert Shirley — roving envoy of Shah Abbas of Persia to the Courts of Europe — and his Circassian wife Lady Teresia, painted in their finery around 1628, and ending with a nougat-coloured David Bomberg roof scene of Jerusalem from 1925.

The heart of the show, however, lies in the 19th century. As new steamship routes opened up the Near East, artists developed a commercial routine. They would travel out in summer, stockpile a collection of sketches and watercolours, return to Britain and, during the winter, turn them into finished paintings to sell at the Royal Academy Exhibition in April, then off they would go again.

Among the jobbing painters there were some more distinguished artists too, notably David Wilkie, David Roberts, William Holman Hunt, Richard Dadd and the central figure of this exhibition, John Frederick Lewis. Lewis had been a moderately successful painter of animal and hunting scenes before he left for Cairo in 1841. He lived there for 10 years, gradually turning native. When he put his knowledge on to canvas, his bravura depictions of light, shade, ­lattice windows and tiles revealed an unexpected world. The Mid-day Meal of 1875, for example, shows a group of venerable men ­sitting on a tiled Egyptian balcony for a companionable repast. Pigeons fly around, horses are readied in the courtyard below, and servants stand about contentedly. Everything is picked out in jewellers’ detail. Contrary to the myth of the East, there is not a woman to be seen, there is no eroticism and no cruelty. It is a scene of civilisation — a gentleman’s club in Cairo rather than Pall Mall.