Barbican Centre, London The avant garde didn’t limit their subversive antics to the gallery. As this fun and fascinating show proves, their sex lives were just as transgressive

Modern love and modern art go hand in hand. Such, at least, is the premise of this surprisingly sexy exhibition that peers into the domestic arrangements of the avant garde.

Redressing the received story of modern art, in which male artists eclipse their female partners, same-sex relationships are glossed over and collaborative unions forgotten, Modern Couples is about relationships between creative people. They like to draw, paint, photograph and wax lyrical – particularly during periods of amorous intoxication, when the other’s body is an erotically charged site. During the height of her relationship with Auguste Rodin, Camille Claudel created tiny models of couples caught in intense embrace. Georges Platt Lynes photographed Monroe Wheeler naked and gorgeously dozing across the rumpled sheets of a disturbed bed. Salvador Dalí and Federico García Lorca exchanged petulant, passionate correspondence.

Facebook Twitter Pinterest Intense embrace … Auguste Rodin’s Je suis belle. Photograph: John Philips/Getty Images

Modern Couples fuzzes the distinction between artworks conceived for a public audience – novels, poems, paintings, sculpture, photographs – and those intended as private. In the case of this exhibition’s more private couples, we see a lot more of the latter than the former. Such is the nature of desires that society’s less progressive elements were yet to accept. Same-sex relationships; menages a trois; extramarital affairs; BDSM: in Modern Couples, all are read not only as grist for the creative mill but as rejection of established social and artistic codes.

A small room is given to the chic lesbians of Paris’s left bank: Romaine Brooks’s elegant, androgynous self-portraits; Tamara de Lempicka’s Les Deux Amies: arch, firm-fleshed female nudes lounging in an amorous haven among toppling architecture and crepuscular skies.

In Lee Miller au Collier, Man Ray portrays Miller with a thick leather strap being held around her neck. Hans Bellmer binds Unica Zürn so tightly in rope that her body looks like flesh trussed for the pot (or like one of Bellmer’s own creepy doll sculptures, with its body divided into jointed segments). Gerda Wegener portrays her partner Einar as Lili: Einar was Gerda’s favourite female model years before she underwent pioneering surgery in 1930 to become Lili full-time, a story told in The Danish Girl.

Facebook Twitter Pinterest Gender games … Claude Cahun, Self-portrait, 1928. Photograph: Courtesy of the Jersey Heritage Collections

So far, so in step with the complex identity politics of our own time. What seems more radical in retrospect is collaborative and egalitarian practice. There are some lovely pairings: works by Sonia and Robert Delaunay, Jean Arp and Sophie Taeuber-Arp, hung side by side, suggesting shared ideas about form and colour. (Arp apparently admired his wife’s “courageous use of rectangles”.)

Natalia Goncharova and Mikhail Larionov espoused a form of abstraction known as Rayism, constructing images from emanations of energy and light flaring out across the surface of their paintings.

Varvara Stepanova and Alexander Rodchenko worked closely (she largely in textile and theatre design, he in photography, though they had a nice line in comic portraits of one another) and certainly understood the equality of their relationship as something intrinsically modern. (After visiting Paris, Rodchenko reported back with horror on the ongoing objectification of women.)

Facebook Twitter Pinterest Lovely pairings … Modern Couples. Photograph: John Philips/Getty Images

Modern Couples accepts amorous complexity that goes well beyond stable monogamy, exploring chains of influence and recombination as dramatis personae move from relationship to relationship. Ben Nicholson from Winifred Nicholson to Barbara Hepworth; Hannah Höch from Raoul Hausmann to Til Brugman. Alma Mahler from Gustav Mahler to Oskar Kokoschka to Walter Gropius.

This last gave rise to one of the exhibition’s ickier moments: the life-size doll that Kokoschka commissioned of Alma after their relationship fell apart. The doll was destroyed: remaining photographs show a cumbersome thing, with curiously furry limbs.

Modern Couples is hugely ambitious, taking in almost 50 relationships. They range from exploitative and abusive to loving and collaborative. Perhaps inevitably, the exhibition is dominated by biography: the amount of explanatory text means it’s often closer to walking through a book than visiting an gallery.

Facebook Twitter Pinterest Stoneblossom by PaJaMa’s George Platt Lynes. Photograph: 1941, Collection Jack Shear

How does the art fit into all of this? Too often, works feel secondary: there’s not much to see of Gustav Klimt, Diego Rivera or Georgia O’Keeffe beyond some fine photographs.

This leaves more space for lesser-known works, among them paintings by Marianne von Werefkin: part of Wassily Kandinsky’s creative circle, her paintings are all ripe intensity and fierce diagonals. Elsewhere, the photographic works of collective PaJaMa offer us erotic treatment of the male nude. Claudel’s sculptures are exciting female-authored evocations of sexual passion.

Modern Couples is a massive enterprise. Jam-packed as it is, each pairing (or trio) can’t but feel underserved: there is so much more to see and to know. It searches for new heroes and new narratives for the story of art in the 20th century, still so dominated by the figures of lone men. For that it should be applauded.