If Tate Britain’s new exhibition was a dish, it would be bouillabaisse, or fish soup: lots of strong colour and taste but made up of strange lumps you can’t identify. The title — Degas, Sickert and Toulouse-Lautrec: London and Paris 1870-1910 — is an odd-shaped mouthful in itself. Only an academic writing his next conference paper could hit upon something as resolutely clunky — inexcusable in an age when publicly funded galleries are meant to be embracing “hard-to-reach audiences”, a quest in which plain, striking communication is what counts.

Furthermore, it’s a cheat. The show includes work by a host of other artists, whose relationship with this great trio is mapped out in detail, sadly blurring rather than enhancing the reasons why these three were chosen in the first place. What’s more galling is that while it serves up a jumbled menu of stunning individual works of art, it falls flat on its face in terms of delivering a coherent, punchy argument. Instead, we’re fed a set of earnestly researched but badly finessed ensembles crammed together that could form a series of mini stand-alone exhibitions in themselves.

But bouillabaisse is delicious more often than not, and the kind of meal-in-itself that the bars and post-theatre restaurants of late 19th-century Paris doubtless excelled in. If you were British, these were disreputable places in a foreign city whose name was synonymous with whores and dissolutes, a decadent citadel where the moral climate was permanently overcast.

If, far more rarely, you were British and a collector of contemporary art, then Paris — or at least the art made there — was really rather remarkable. First, it chucked out history, ancient and modern (no nymphs or generals please), and made the present the subject, catapulting the places of everyday city life — theatres, music halls, cafés, bars — into the frame. Second, it made the urban crowd — the people watching the performance, the customers eating and drinking — part of the subject.

Walter Sickert’s studies of music-hall life, with their front-of-stage uplighting, floozily dressed singers and balconies full of heckling chaps, are irredeemably modern for the way they equated spectatorship with performance. These remarkable images are, as Sickert once said about Lowering the Curtain, a picture of ballet life by his hero and friend Degas, “fragments of a thing seen”, cropped meditations on the fleeting experience of life in the emerging modern city. Nothing, it seems, was unworthy of an artist’s attention.

This seismic shift in thinking — one that echoed the metropolitan public’s restless desire for social and political change — is never more apparent than in Degas’ L’Absinthe, painted in 1875-76, which you find a third of the way into the show. The picture created a media storm when it was exhibited in London in 1893, and anyone following the recent Kate Moss saga may find it especially interesting.

Here was real life: a man and woman, emphatically not a couple, facing the solitary truth of their place in the world. No whimsy, no attendant angels, nothing. And the agent behind this private hell? The glass of absinthe, the crack cocaine of the Victorian era, its addictive potency glowing with green malevolence. According to the Victorian artist Walter Crane this picture offered “the Adam and Eve of a new world of aesthetic pleasure, degraded and not ashamed, a paradise of unnatural selection”.

When it surfaced that the woman depicted, taken by all to be a prostitute, was in fact an actress, one Ellen Andrée, and the uninterested man beside her an etcher called Marcellin Desboutin, the outrage was all the greater as critics denounced Degas for unmasking what they thought was a real scandal of unsavoury association. That he had merely asked both of them to model for him never occurred to these moral harpies. For me, this is the first true picture of the modern media age, an image charged with tensions about documentary authenticity, moral probity and supposed celebrity revelation, where the image-maker plays a knowing game in which the delicate line between the public and private world has been deliberately blurred.

For all the later hoo-ha about the painting, it had been a British collector, Captain Henry Hill, of Brighton, who had bought L’Absinthe fresh off the easel, and in providing evidence of the booming market for French avant-garde art in Britain, the exhibition succeeds in showing how stereotypes (boring old Britain versus fashionably risqué France) should be treated with caution.

Whistler, a creative revolutionary, lived in London, as did Tissot and a host of other continental artists who eschewed the doctrinaire atmosphere of Paris for the mercantile opportunities of London. That said, it’s amusing to hear of Edward Burne-Jones, that purveyor of pseudo-medieval pageantry in which thin sickly girls mope around in marshes (an early manifestation of heroin chic?), attacking Degas for using “fag-end girls” in his studies of ballet-school rehearsals. When you meet Degas’ Little Dancer aged fourteen, a bronze statue two-thirds life-size complete with real faded tutu, you can smell the greasepaint and sticky pointes.

Instead of capitalising on the emotional and psychological accent given by L’Absinthe, the following rooms collapse into a narrative muddle, with a gallery of delicious beau-monde portraits somehow leading on to what might as well be a separate exhibition of pastels and lithographs of theatre life by ToulouseLautrec. What a pity the curators didn’t explore how and why the dangerous instability of “red carpet ” society appealed to artists who were both observers and participants in this volatile theatre of chit-chat.

The worst mistake, however, lies in the choice of Degas’ The Rape and Sickert’s Ennui to end the show: they make a great pairing, each an essay in gender prejudice and spatial atmospherics, but the tempo is wrong, and by posing so many unanswered questions, they merely leave a strange taste in the mouth.

Degas, Sickert and Toulouse-Lautrec: London and Paris 1870-1910, is at Tate Britain, SW1 (020-7887 8888), from tomorrow