Rodchenko & Popova: Defining Constructivism, Tate Modern, London

'Either do houses or do art, but not both,' snapped one critic. But these avant-garde Russians paved the way for Warhol

(ANDY RAIN/EPA)

Of the ghosts you might see wandering Tate Modern's show Rodchenko and Popova: Defining Constructivism, the last you'd expect would be Andy Warhol's.

The Russian duo were models of earnestness. In light-hearted moments, Rodchenko was prone to such utterances as: "Russia has given birth to her own art, and its name is non-objectivity." Even Popova's headscarves were political. Then there was the pair's Bolshevism. It is hard to imagine a milieu less sympathetic to Warhol than theirs, or a mode of art-making less attractive. And yet, here is Andy's shade, fright-wigged and ashen, scoping Popova's Painterly Architectonics with a glint in its eye.

To recap. Aleksandr Rodchenko (1891-1956) and Lyubov Popova (1889-1924) were among the most brilliant of the artists who shaped the Russian avant garde. In the years around the revolution, everything was up for grabs. The world was to be redefined and so, too, was art's place in it. There was to be no more sighing in garrets. The brave, new, proto-Soviet artist was socially and politically engaged, his (or her) profession akin to that of an engineer. True to revolutionary form, Constructivism welcomed women as equals to its hard-hatted ranks – the point, presumably, of showing Rodchenko with Popova rather than with his wife, the artist Varvara Stepanova.

This kinship with engineering coloured the art the Constructivists produced – works whose faktura (or means of making) was to be obvious from the way they looked. And it was not just insistent handmadeness that suggested manual labour. Stand in front of Popova's Space-Force Constructions of 1921 and you'll find yourself thinking of scaffolding. The bituminous black of the horizontals look like roofer's tar; the stuccoed white verticals are not so much painted as rendered; the plywoody-brown of the picture's background is, in happy fact, plywood.

By the lights of the Constructivist project, art had to be everyday: the First Working Group of Constructivists, to which both Rodchenko and Popova belonged, sacked Kandinsky as chairman for being too "mystical". In return, and in the spirit of the times, other artists denounced them as mere artisans. The term "Construction Art", coined by Kazimir Malevich, was not meant as flattery; Naum Gabo snapped: "Either do houses or do art, but not both." Unrepentant, Rodchenko and Popova set about making work that worked. One of the most engaging pieces in this show is the reconstruction of a sculpture by Rodchenko that doubles as a newspaper kiosk.

Malevich's mistake was to assume that the Constructivists' pushing of the boundaries of art was a one-way street. Actually, art's engagement with engineering was symbiotic. The elegance of the work in the first rooms of this show is not so much Constructive as deconstructive, Popova's Painterly Architectonics stripping the act of painting down to the nuts and bolts of plane, form and colour. This tendency reaches its inevitable end in 1921 with Rodchenko's showing of a monochrome trio, Pure Red Colour, Pure Yellow Colour and Pure Blue Colour. Looking at these, the artist announced "it's over", and moved into working in three dimensions.

You may be wondering where Warhol's ghost has got to in all this, and it is to be found skulking in the room beyond Rodchenko's one-note threesome. In a sense, the Tate's show ends unhappily. We know what happens next: Popova, dead of scarlet fever at 35; Rodchenko, charged with formalism in the late 1920s and expelled from the inner circles of Soviet art, finishing his days taking photographs of sporting events; the Constructivist experiment concluded by 1935. And yet the astonishing thing about Defining Constructivism is the sense that its story isn't over.

While Rodchenko and Popova may have been emphatically of their place and time, their work has proved boundless and timeless. It is a short step from Rodchenko's Spatial Constructions to the buildings of Zaha Hadid; from the impersonality of Popova to the made-at-a-distance work of Sol LeWitt or Keith Tyson. The pair's influence is to be felt in the oddest places, and none odder than in Warhol's Factory.

The ninth room of this show is dedicated to their work for Lenin's New Economic Policy, much of it in the form of advertising – a poster for rubber galoshes stays potently in the mind. That fine art could be stretched to include Coke bottles and soup tins seemed revolutionary enough when Warhol did it in the 1960s. And here, half a century before, is Rodchenko's poster for Red October Cookies, as clever as a Warhol and as modern.

Tate Modern, London SE1 (020-7887 8888), to 17 May