The Finnish painter Helene Schjerfbeck is not exactly a household name in Britain – and there’s no reason she should be. This is the first UK solo show of her sort-of expressionist works and it’s strictly for the dutiful. It might serve to cool you down on a hot day, though. Schjerfbeck’s uninspired miserabilism is a cold shower of second-rate art.

Born in Helsinki in 1862, Schjerfbeck had a long painting life that only ended with her death in 1946, her easel at her bedside. She is almost the exact contemporary of the Norwegian Edvard Munch and, like him, she painted the long dark night of the Nordic soul. However, in her art this teeters on bathos and descends into embarrassment. The curators have included three portraits of her mother, one a heavy-handed homage to Whistler’s Arrangement in Grey and Black No 1. The artist’s daughterly devotion is clear, yet there’s nothing in them to make the viewer share that interest. It’s hard to know why we need to intrude on this private world.

Daughterly devotion … My Mother, 1909. Photograph: Private collection/Finnish National Gallery

Those paintings are from Schjerfbeck’s best period, before the first world war. She got much worse with time – either that or the curators have served her badly. For there is an entire roomful of portraits in which she imagines her neighbours and relatives as 1920s flappers and dandies. The exhibition sees these as important, even radical, because she’s playing with identity. If she had been a photographer this might work – the show seems to want to make her into a masquerading subversive, like the surrealist photographer Claude Cahun, but painting works differently. It cruelly exposes the least hint of superficiality and silliness. Paintings such as The Circus Girl, a 1916 portrait of a young woman wearing clown-like lipstick, and The Motorist from 1933, in which the artist’s nephew poses as a suave high society character (so suave he has a car) are hardly revolutionary comments on the fluidity of the self. They are just very bad paintings, technically and intellectually inadequate.

This is sad, because Schjerfbeck started out with ability, talent and even a vision. Her 1884 painting of Helena Westermarck is a moving and memorable image of a woman who can’t bear to look at us directly. Clothes Drying is a painting of laundry laid out on the grass – and it’s strangely fascinating. Equally devoid of human figures and full of mystery is The Door, in which sunlight creeps between the edges of a gothic entrance to a church interior.

A sense of deathly stillness … Schjerfbeck’s Shadow on the Wall (Breton Landscape), 1883. Photograph: Niemistö Collection; photo: Finnish National Gallery

This was painted in Brittany and Schjerfbeck shows a real feeling for the potential of the impressionism she encountered in France to explore the quiet, introspective recesses of experience. In Shadow on the Wall: Breton Landscape (1883) she captures a deathly stillness in the midst of rural beauty. Paradoxically, it is as a late 19th-century realist that she can explore the soul most effectively.

In presenting Schjerfbeck as a go-getting 20th-century modernist, this exhibition dwells not on her early strengths but on a long decline. It also includes a room in which she charts her physical decay in a series of brutally honest self-portraits. They’re certainly brave. Her last paintings of herself are skull-like. She stares at her imminent death in the mirror. While impressive, the effect is bizarre rather than tragic. From the 1900s, Schjerfbeck adopted one style after another, from Munch’s symbolism to Schiele’s expressionism, but the results look like a futile fight to keep up with artistic fashion. It’s depressing and pointless to drag this stuff up from the storeroom of art history, where it belongs.

• At Royal Academy, London, from 20 July to 27 October.