Right now, you cannot get away from the Russians. Their artistic presence has dominated the year so far.

Come to think of it, they dominated much of last year, too. If you’ve been to an auction house recently, you will not need me to point out that the Russians are everywhere. They prowl around the back of the auction room in their offensively casual tracksuits and trainers, bidding up whatever it is you want to unbuyable heights, then buying it anyway. These guys have no limits. And, as another Rodchenko photograph or El Lissitzky book cover eludes your grasp – you will have noticed by now that this is personal – you have no choice but to slump back in your seat and accept failure. Again.

All this is terrible news. Far, far better that Rodchenko’s photographs end up back at my house, where they will be properly appreciated as some of the 20th century’s most iconic and revolutionary produce, than that they jostle hopelessly for pertinence with framed Chelsea programmes and signed mugshots of Frank Lampard on the walls of Roman Abramovich’s yacht. The Russians are buying back their heritage with all the warmth and charm of a house repossession in Solihull. But there is an upside. This avalanching of Russian money into the British art world has resulted in the arrival here of more Russian art than ever before. And, providing you pick your way through these vulgar Volga outpourings with more discernment than the Soviet bulk-buy-ers themselves appear to show, there is much to savour. Like the stimulating Rodchenko display that has arrived at the Hayward Gallery – made possible, I read, “with the support of Roman Abramovich”.

Rodchenko was one of the heroes of European modernism. Or so I have always believed. He was born in St Petersburg in 1891; his dates coincided perfectly with the Russian revolution, and the spirit of his times seemed to flow through him in a particularly pure form. At first, this happy congruence led him to great excitements and achievements. Then it betrayed him and clogged his veins with tragedy. So, his story is a hugely symbolic, as well as an artistically gripping, one. And the Hayward tells it well.

Rodchenko was one of those artists who was good at everything he tried: a painter, stage designer, poster-maker, book illustrator and effective propagandist, first for Lenin, then for Stalin, and always for the cause. But this particular show, the first big Rodchenko exhibition in Britain, concentrates on his photography, and seems to prove that it was simultaneously very revolutionary and very basic. For instance, we catch up with him in 1925, and a famous image of a woman in a headscarf cupping her hand to her mouth and screaming out the word “BOOKS” (or, inRus-sian, “ KNIGI”). You might recognise the headscarved shouter from the cover of Franz Ferdinand’s second album, where she appears in a crudely adapted form yelling out the band’s name. Thus, what began in Russian revolutionary times as a heroic exhortation to the world to read more books has ended up, in our times, as an ad for a noisy indie band from Glasgow.

Never mind. Combining the picture of a woman shouting with the words she shouts is a strikingly simple idea, yet Rodchenko’s infallible instinct for dynamism and the addition of fine swathes of coloured constructivist typography, set at jaunty angles, result in a memorably rousing image.

The Hayward is canny enough to open its proceedings with a busy roomful of these obviously exciting photomontages, rather than turn immediately to Rodchenko’s pure and tiny black-and-white photography. With the best will in the world, there are only so many thrusting factory chimneys and gleaming rows of identical Moscow machine cogs that even I, a fan, can look at before the fog of Soviet boredom rolls in. Besides, one of the key conclusions reached by the show is that Rodchenko never really became a pure photographer. In his hands, the medium was always under firm instructions to make you do things, want things, see things. His photographs always had an ulterior motive.

Take his famous portraits of that dramatically moody Russian poet Vladimir Mayakovsky, which pop up early in the show and are among its greatest joys. Mayakovsky was a fabulous-looking guy. Shaven-headed. Intense. He wore battered three-piece suits, a mean cigarette usually dangled from his lip, and his unwavering stare comes at you as fiercely as an unleashed Soyuz missile. It’s hard to imagine a more dramatic presentation of the artist as warrior. Yet the catalogue tells us Mayakovsky’s friends complained that Rodchenko was lying about their man by never showing him smiling or larking about. They didn’t recognise this super-stern Mayakovsky. He wasn’t real.

It’s the story of the whole show. What you never get here is photography as a responsive or sensitive medium, a mirror to reality. Not for a moment is the dull Soviet world allowed to remain a dull Soviet world. Wonky angles. Alarming tilts. Crazy vistas. Jagged shadow patterns. Skyscrapers viewed from above. Factories viewed from below. An abruptly foreshortened sportsman. A dramatically diagonal musician. There is hardly a photo here that isn’t trying something on. Not once do you feel Rodchenko has stopped to capture something that actually happened to catch his eye. Instead, photography is being relentlessly employed to conceal the truth. And Hitler was surely never more right than when he pointed out that the masses “will more easily fall victim to a big lie than to a small one”.

Rodchenko took up photography only in the 1920s, after a brilliant spell as a painter. (If you want to see his paintings, there are some in the Royal Academy’s marvellous From Russia show.) And he did so because he believed photography was the most appropriate artistic medium for the times ahead: fast, mechanical, futuristic. So, all the insights he had gained as a painter were unleashed on his photographs, and the results are invari-ably dynamic and inventive. Just as Stalin had his five-year plans for the future of Soviet society, so Rodchenko had his carefully considered path for the future of photography. And, for most of the show, it makes for an exciting journey.

I had a lot of fun, too, noting how his quick-acting visual tricks were soon picked up by others. It’s clear, for instance, that Leni Riefenstahl’s sporting masterpiece Olympia, made for the Nazis in 1938, owes most of its best cinematic inventions to Rodchenko’s Soviet sporting photography. But it is here, in the early 1930s, with Stalin consolidating his power and Rodchenko named as a decadent “formalist”, that the show begins to peter out. In fact, Rodchenko lived on until 1956. But the final body of work this event unveils, a soft-focus attempt, in 1940, to capture the sadness of the Soviet circus, is the output of a man whose spirit has been crushed, as well as his vision.

Downstairs at the Hayward, an ambitious but doomed theme show called Laughing in a Foreign Language continues to explore the way other nations see things. The topic this time is laughter: what other countries find funny in art, and why. It is doomed because deciding on what is funny in art is impossible enough in your own culture without crossing your fingers and dragging in China, Switzerland, Japan, South Africa and the rest of this show’s unfortunate exhibiting nations. There isn’t a hope in hell of anyone here coming to a worthwhile conclusion about any of this.

Alexander Rodchenko: Revolution in Photography (until April 27) and Laughing in aForeign Language (until April 13)are at the Hayward Gallery, SE1

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