The Moulin Rouge, a dance hall in late 19th-century Paris, has been depicted in more than one film. I feel compelled to add "and sensationalised". But looking at the way the nightclub's famous habitué Henri de Toulouse-Lautrec portrayed the fin-de-siècle denizens of nocturnal Montmartre, it's clear that film-makers have been sanitising the story. Neither Baz Luhrmann nor John Huston came anywhere near the true wildness and strangeness of the real Moulin Rouge.

You can see the original, raw reality of Toulouse-Lautrec's Moulin Rouge in an exhibition at the Courtauld Gallery, which closes on 18 September 2011. Summer visitors to London should put it on their itinerary, especially as the £6 admission also gets you into this gallery's small-but-exquisite collection of artistic masterpieces, which includes Manet's highly relevant A Bar at the Folies-Bergere.

The exhibition concentrates on the sickly southern-aristocrat painter's friendship with a thin, nervous dancer called Jane Avril. Hospitalised for mental illness as a teenager, Avril was mocked by some as a crazy dancer whose legs spun all over the stage while her face remained a mask of misery. But in Toulouse-Lautrec's portraits and posters, she is at once intensely lonely, mysterious and – blatantly – his object of desire. The bony beauty of Avril blazes eerily in his supercharged vision. The power of Toulouse-Lautrec is that the more seedy and unglamorous he makes places and people look (for he is a savage realist, and faces in his pictures are waxen with pain) … the sexier it all is.

Truth is far stranger than fiction in this exhibition. Toulouse-Lautrec's 1892-5 painting At the Moulin Rouge has been loaned from the Art Institute of Chicago. It's a masterpiece. In the foreground, a huge green face, caught in the spooky lights, menaces you. At a table beyond, a gathering of bohemians and dancers whiles away the night. In the background is the dancer La Goulue, while the room itself melts into a curtain of abstract colour. The scene is somehow more exotic and more exciting than any recreation in popular culture. In his portraits of Avril inside or outside this and other Montmartre haunts, her bleak beauty seems impossible for any actor to recreate.

The explanation is twofold. First, Montmartre was a dangerous place in the 1890s and yet the memory of it, preserved as it is today as a tourist attraction, is soft and nostalgic. This was a world pitched between the brothel and the hospital – there was nothing coy or cosy going on. Second, the way Toulouse-Lautrec depicts his chosen milieu is modernist. His portraits teeter towards abstraction, even as they record violent reality in acid colours. His posters, certainly, are truly abstract.

Toulouse-Lautrec's Montmartre was an intense place, but his art adds another dimension of fantasy and feeling. The cocktail is a delicious artistic poison. See this, and lose your innocence.