Along with more sinister institutions nearby, the towering, crenellated Red October chocolate factory was one of the most celebrated landmarks of Soviet-era Moscow. Throughout the 20th century, its candies, cocoa and biscuits marked out the fortunes of the state - and, more bizarrely, those of its artists. When the factory was seized by the Bolsheviks in 1917 - and named first State Confectionery Factory No 1, then the more evocative Krasny Oktyabr - some of the finest artists of the revolutionary era were set to work decorating and promoting its products. Between 1923 and 1925, the avant-garde artist Alexander Rodchenko and the poet Vladimir Mayakovsky, working together as "Mayakovsky-Rodchenko: Advertising Constructors", created more than 150 advertising and packaging designs for Red October and other state companies. In the bright dawn of the revolution, it seemed that even chocolate bars could be part of the new order: little packages of correct social values and radical aesthetics.
Red October still stands under its famous sign by the Moscow River, but its face has changed along with the city's. In 2007, the last workers were transferred to new factories in the suburbs and the factory was turned over to a $2bn luxury-flats development scheme, currently stalled by the credit crunch. But there are still artists around. Outside towers a retro-nationalist monument, erected in 1997: a 96 metre tall, breathtakingly ugly statue of Peter the Great by the wealthy Georgian-born sculptor Zurab Tsereteli, a close friend of the mayor of Moscow. Though Red October is largely empty - single bulbs illuminate cracked tile floors and rusting rows of workers' lockers - an upstairs floor is now given over to Baibakov Art Projects, a foundation run by Maria Baibakova, the US-educated, 23-year-old daughter of a former mining magnate. Baibakova, playing with a necklace from which dangles a single golden bullet, leads the way briskly through preparations for "invasion: evasion", her inaugural exhibition of contemporary Russian artists. One installation is a tangle of paint-stained stepladders and champagne flutes. "It's about what comes before and after the art, the preparation and the private view - it's about doing away with the art altogether," she explains.
The factory's latest incarnation could not be more out of step with the hopes of its revolutionary designers. Along with his friend and collaborator Lyubov Popova, Rodchenko was one of the most influential avant-garde artists of early Soviet Russia. "Rodchenko and Popova: Defining Constructivism", opening at Tate Modern next month, traces their unfulfilled dreams for their country and their enduring impact on 20th-century art and design.
By 1917, the two artists, despite their different backgrounds - Rodchenko was from a working-class St Petersburg family, Popova the daughter of a wealthy Moscow industrialist who indulged her love of painting - were united by their fascination with new art and new ideas. Popova had spent much of the previous decade travelling and studying in Russia and Europe, absorbed first by the Orthodox icons in Russian monasteries, and then by the novel, striking and aggressive work of the cubists and futurists in France and Italy.
Then came the October Revolution. For progressive artists as much as political leaders, it was a uniquely exhilarating moment. Their work was no longer to be confined to the elite realm of galleries and studios. The entire fabric of everyday existence - from mass transport and housing projects to teacups and book jackets - was to be redesigned to serve a new vision of Russian life. The result was an explosion of creativity: from magazine covers to stage set designs, the work at the Tate crackles with intellectual excitement.
In addition to their utilitarian projects for the young state, Rodchenko and Popova continued to work out their artistic principles through drawing and painting. Between 1917 and 1921, they produced canvases, collages and sketches full of a rough-and-ready, kitchen-table energy. The work combines bold colours with geometric forms and rushing diagonal lines: rather than appearing a flat, static surface, the canvas became the arena for a succession of colliding forces barely kept in two-dimensional check. Popova produced her Painterly Architectonics sequence (1917-18), while Rodchenko worked on his Black on Black series (1918), a reaction to Kazimir Malevich's Black Square (1913) which, with its mechanically applied shades of black paint, attempted to achieve an industrial impersonality. He also experimented with "spatial constructions": brightly coloured mobiles and forms that bridged the gap between painting and sculpture. Popova's Spatial-Force Constructions (1921), which left areas of their plywood backboard bare and incorporated wood dust into the paint, stripped from the "canvas" the last remnants of conventional artifice and illusion.
In addition to their private practice, both artists had a public role to play. In 1918, the Bolshevik government began to buy avant-garde works for distribution to provincial museums, and Rodchenko was soon appointed director of the Museum Bureau and Purchasing Fund. Artists were no longer to be solitary creators engaged in self-expression, but useful employees of the state. At first, collaboration on revolutionary projects flourished: Rodchenko's famous photographs of his fellow artists show them gathered for tea with friends and family or examining work in each other's studios. However, arcane ideological differences soon divided the art world into a very Soviet chaos of competing working groups and institutions.
Despite their convictions, Rodchenko and Popova were pursued by anxieties about their two-dimensional work: could it justify its place in a communist society? Should the individual artist seek to express himself through an aesthetic object? Shouldn't artists involve the workers in any "art" they produced? In 1921, they announced the "last constructivist painting show", the "5x5=25" exhibition, in collaboration with the painters Alexandra Exter, Alexander Vesnin and Rodchenko's wife, Varvara Stepanova. Rodchenko's contributions included the movement's first monochromatic paintings: a triptych of "smooth boards" mechanically covered in a single pigment each - Pure Red Colour, Pure Yellow Colour and Pure Blue Colour (all 1921) - intended to do away once and for all with the individuality of artwork and artist. "I reduced painting to its logical conclusion and exhibited three canvases: red, blue and yellow," he said. "I affirmed: this is the end of painting."
Painting thus despatched, the artists turned their attention to other media. Popova produced designs for theatre sets, furniture, book jackets and posters. With Stepanova, she worked at the First State Cotton-Printing Factory, designing dresses (though their severe lines proved unpopular with the stubbornly comfort-seeking proletariat) and beautiful, geometric-patterned fabrics, only fragments of which survive. "No single artistic success gave me such profound satisfaction as the sight of a peasant woman buying a piece of my fabric for a dress," wrote Popova of her work there. Rodchenko began to collaborate with Mayakovsky on both advertising projects such as their Red October chocolate campaigns and the Lef and Novyi Lef magazines of revolutionary criticism and poetry. His use of bold colours, clear shapes and block lettering laid the ground for much 20th-century graphic design. A particularly striking example is his fiercely unsentimental black-and-red catalogue for a retrospective held following Popova's early death from scarlet fever in 1924.
The death of Lenin, in the same year as Popova, marked the onset of hard times for her colleagues. From 1925, Rodchenko devoted himself increasingly to photography, focusing on new Soviet architecture and portraits of his friends. In 1932, Stalin banned independent artists' groups and several of the constructivists - Aleksei Gan, Boris Kushner, Gustav Klutsis and Nikolai Chuzhak - were shipped to their propaganda such as his beautifully composed series on Stalin's White Sea Canal, the construction of which claimed the lives of thousands of workers.
The constructivists' dream of a fairer, more beautiful Russia foundered. Many of their projects - such as Popova's designs for a vast street spectacle enacting "The Struggle and Victory of the Soviets" - never came to fruition. Rodchenko's famous model Workers' Club, created as a showpiece for the 1925 "International Exhibition of Modern Decorative and Industrial Arts" in Paris, was never built in his own country. In central Moscow, six-storey billboards for Rolex, Bulgari, BMW and Toshiba have taken the place of his state advertising posters.
Only the slightest traces of the constructivists' utopia remain. At the Likhachev Palace of Culture, an austere concrete block not far from the Red October factory, workers eat fried eggs in a battered 1930s cafe designed by Popova's friend Viktor Vesnin. At the Tate show, you can see the blueprints for this future that never was.
"Rodchenko and Popova: Defining Constructivism" opens at Tate Modern, London SE1, on 12 February. For more details log on to: www.tate.org.uk