In the most staggering room in Paula Rego’s retrospective of seven decades’ painting, women crouch, crawl, kneel and sleep. One, called Dog Woman, goes down on all fours and contorts her face as if she is barking or howling. In the neighbouring picture, Bad Dog, a woman is seen from behind as she assumes a similarly abased position on a bed. There are no men in any of these paintings but the strange poses into which the women are twisted could be dictated by an invisible man, grunting commands. Then again they might not. They might be suffering for God. Since these two scenes of torment and anguish, expressed in a physical casting down, seem to echo the 17th-century Spanish artist Jusepe de Ribera’s paintings of the punishments of the damned. Rego was born in Portugal in 1935 and her art is steeped in Iberian experience, from Catholicism to 20th-century dictatorship. It is a distinctive blend of that history and the meat-and-potatoes realism of the UK, where her parents sent her to escape Portugal’s authoritarian regime: a dream marriage of Hogarth and Ribera, with Goya and Buñuel under the bed. That’s made nicely explicit by a trilogy “after Marriage a la Mode by Hogarth”. Like Hogarth, Rego is a narrative painter, telling tales on canvas. But her stories are surreal and mysterious. Freaky hairstyles, uneasy glimpses in mirrors, and a sense that everything is being staged in a cluttered rehearsal space leave you interpreting a poetic enigma. In the final scene, the bride cradles her husband like the Madonna supporting the dead Christ. Rego has had a dramatic life. As a refugee, in 1951 she made her home in London and married a fellow artist, Victor Willing, who died from complications to multiple sclerosis. That’s the source of her Hogarthian pietà. But whether her art is autobiographical, or simply provides material for her fictions, is deliciously, disturbingly impossible to resolve. Willing appears twice in her big dreamy 1988 painting The Dance, once with her and also with another woman. This painting is about the past, about the nostalgia that reshapes memory even as it preserves it: the dancers have gathered on a beach in the moonlight, in old-fashioned clothes, under a castle that adds a sinister touch, as if their moment of tranquil happiness is a reprieve from something brutal. The Dance is part of a group of bold 1980s masterpieces that all share this spine-tingling nostalgia. They are set outside time, in a place where extreme conservatism, even fascism, produces peculiar corruptions and perversions. In one tall canvas, a young woman dressed in red is kneeling down to lace the well-polished shoe of a uniformed young man. Her stiff leather handbag, open to reveal a crimson interior, rests beside her gloves on the ground. As she does up his laces, his white-gloved hand tenses crab-like, while his face melts in ecstasy. It’s an eyeful of sick innuendo and surrealism even before you read its title: The Cadet and His Sister. The Policeman’s Daughter, meanwhile, depicts a young woman in a white dress polishing her father’s jackboot. Her bare left arm is deep inside the high black boot, so it seems to merge with and enfold her as she shines it, her eyes cast down, keeping her thoughts private. All the paintings in this spectacular series from 1987-8 suggest an oppressive, dishonest society where kinky complications accumulate like dust on a patriarch’s boot. She’s a magic realist in paint – or rather, paint and pastels. For pastel has become Rego’s main medium since the 1990s. Her pastels, too big and painterly to be called drawings, have a physical intensity, at once soft and rugged, that makes bodies and faces explode off the wall. Rego, it turns out, has done her greatest work since the 1990s. There is a tragic force to these later, often isolated figures that takes us beyond storytelling into a realm of baroque existentialism. The Cell, from 1997, depicts a man in prison, lying downcast on a bleak bed – or is he a model in the studio, imprisoned by the artist? Nearby a woman kneels by her bed in underwear and presses her face against a dress laid on the red silk bedcover. Rego is phenomenal but this exhibition won’t let you immerse yourself in her world. Every room has walls painted a different colour, in a random, neurotic assault. Who chose turquoise for the room where Rego’s grand 1980s scenes hang? Who, for that matter, would hang any paintings against such a colour? This may seem trivial but it’s revealing. For it shows how remote this museum’s heart is from the art Rego makes – all that old stuff on canvas and paper. And there hangs a story of shame. Rego hit her stride as a painter not long before Damien Hirst’s generation cast painting aside. You may not be familiar with her great works from the 1990s. Of course not. They were drowned out by all the new sensations. If you can ignore the intrusively coloured walls it is harder to avoid the unhelpful wall texts that keep trying to batter her subtle strangeness into crude political messages. You are told repeatedly to see the art as protest. It is not. It is art. And when you overcome the unnecessary irritations, and reach that incredible Dog Woman, you will find that it is great art. Paula Rego is at Tate Britain, London, from 7 July to 24 October.