Exhibition review: Hannah Höch, Whitechapel Gallery, London, until March 23 2014

She has inspired major retrospectives in Paris and Berlin (1976), New York (1997) and Madrid (2004). But it has taken London more than three decades since the death of Hannah Höch to catch up with her genius for collage.

With a background in fashion, she may still be the only person to have ever written a manifesto for embroidery. In 1918 she insists the purpose of this gentle artform is “not to decorate”. She made satire during the Weiner Republic and, during World War II, beat a retreat to a small house outside Berlin. Because Höch was politicised from the get go.

In 1946 she makes a piece called Beautiful Snares, pasting down fireworks alongside a dandelion fruit and a fisherman’s keep net. War-torn Europe was no place for pretty pictures, and so Höch deals in the strange, the startling, and sometimes the comic.

An example of all three qualities appears in 1931 in a piece called The Small P. Here you find the unfurrowed brow and slicked back hair of a matinee idol integrated with the face of an angry and tearful child. It is an inner child, perhaps, and there is nothing beautiful about it.

This show lacks the gloss you might find in any of today’s magazines. So work by Höch can look as dated as her materials. But once you connect with the impulse behind her witty juxtapositions they reveal themselves as fresh and enduringly relevant.

1923 work High Finance features a pair of venerable statesmen with heads cleaved in two by the twin barrels of a shotgun. And coming over the horizon is an ominous military truck. Perhaps more than ever, we live in a world where money and military intervention go together.

The gallery layout at the Whitechapel well suits this artist’s divided career. Climbing stairs to Gallery 9, the interim years of National Socialism accounted for by a private Album which Höch compiled around 1934. It was a scrapbook of images which show her fascination with mass media such as it was at the time.

Höch’s output at this time was limited, so it is not hard to imagine her escaping the daily realities of war and war preparation by losing herself in this project. When the Allies liberate Berlin she writes in her diary: “In my soul there is a calmness, such as I haven’t felt for many years.”

The same year she makes a work called Dove of Peace through which one such bird flies unfettered in a grey sky. An array of thrusting metal in the foreground suggests mortar guns, girders and even organ pipes. Yet the effect of the weightless dove is to quieten the whole composition.

But despite the import of many works which engage directly with history, Höch also has a mile wide playful streak which probably comes with the territory in collage. She could be cute as well as acerbic; works like The Basque and Good People from the Mountain are a delight.

In the former, a bird of prey is given human eyes, kissable lips and a jaunty beret. In the latter, a pair of gargoyles throw open their hands in welcome. Their mountain is a barren and uninhabitable rock in the background and one wonders on what terms we meet these 'good people'.

Writing in the show’s excellent catalogue, art historian Deborah Lewer does point out that Höch would sign herself H.H. and when spoken by a German this sounds like Ha Ha. She also quotes artist Otto Pankok who wrote, in 1922: “Our age is terrible and deadly; so too is its art, so too is its laughter".

It reminds you that Höch emerged from the most irreverent art movement of the 20th century: a selling point for this show. Dadaism was widely considered a man’s game, but Höch was very much an equal partner in the movement, friendly with Kurt Schwitters, and in dialogue with George Grosz and Theo Van Doesburg.

Dada scandalised the times in which Höch came of artistic age. But if there is any scandal attached to the current show at the Whitechapel, that could only be how long we took to give this inventive, lively and conscientious artist her dues.

• Open 11am-6pm (9pm Thursday, closed Monday). Admission £6.95-£9.95. Follow the gallery on Twitter @_TheWhitechapel.

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