Last year the British Museum did itself proud with The American Scene: Prints from Hopper to Pollock. Uncovering the thick vein of Marxism and political commitment among US printmakers in the first half of the 20th century, it proved a surprising hit and attracted more than 400,000 visitors.

Now we have its sequel, Revolution on Paper: Mexican Prints 1910-1960, an exhibition of broadsheets, posters and fine art prints that takes us across the Rio Grande to revolutionary Mexico, where printmakers were fired by the same passions as their US counterparts, but had the luxury of expressing them from a position of considerably more political strength.

When Emiliano Zapata’s uprising, which began in November 1910, finally overthrew the dictatorship of Porfirio Diaz, Mexican artists were recruited en masse to serve the 20th century’s first successful socialist revolution. Gigantic murals became the cultural trademark of the first revolutionary years, most of them conceived by three artists: Diego Rivera, David Alfaro Siqueiros and José Clemente Orozco – known collectively as “Los Tres Grandes”.

Many younger artists found work as their assistants but, feeling creatively stifled by the dominance of the Big Three, moved on to printmaking as a smaller but equally useful form of socialist art. They were partly inspired by a very different Mexican tradition: the work of a pre-Revolutionary artist of relatively crude and populist style, but with a spirit unmistakably in tune with the times. His name was José Guadalupe Posada and a generous sample of his output opens this exhibition.

Posada earned the respect of later Mexican printmakers less by his visual style, which is largely that of a comic artist, than by his subject matter. From 1880 onwards he specialised in a form of ephemera unique to Mexico, the calavera (skeleton) broadsheet, which he produced every autumn to coincide with the time when Mexicans celebrate the dead’s annual return to earth, the feast of All Souls. A typical Posada broadsheet is of doggerel verse illustrated with caricatures of skeletons, the words and graphics satirising the manners and attitudes of the living through the dead.

Posada dressed his skeletons up, gave them hats and moustaches, and made them behave in ways that reflected prevailing social conditions. So the rich skeleton wears a top hat, drinks from a stem glass and retires beneath his personal tombstone, while the peasant skeleton makes do with a sombrero, an earthenware beaker and an unmarked grave.

Posada is not merely poking fun. He is contradicting the conventional idea that death is the ultimate leveller, and so radically subverts the deeply Catholic culture of Mexico. Made for mass consumption, these broadsheets portray the dead world as if it were just like the living one. By giving the lie to priests who told the people their sufferings would be rewarded in heaven, Posada’s message was that the only salvation the poor can expect is in the here-and-now, through political action and social revolution. It earned him the respect of Mexico’s post-revolutionary artists, who make up the rest of the show.

Posada’s followers are obviously far more sophisticated than he. Between the wars each of the Big Three – fierce rivals politically as well as artistically – developed vivid graphic languages of their own, but none of their prints in this show look as absolutely singular and vibrant as the work of their slightly younger contemporary Rufino Tamayo.

His woodcuts, though less overtly political, are impassioned celebrations of peasant life, in which sweated labour and poverty are visibly engrained in the image. Eventually, Tamayo became a world-famous artist in his own right, having long outlived the Big Three at his death in 1991.

Like every left-wing group in the world, Mexican artists were profoundly affected by Franco’s rebellion against the Spanish republic. One lithograph by Francisco Dosamantes, entitled “Bombardment, Spain, 1937” and dominated by a woman’s sculpturally monumental head, which two shellshots have punctured, was produced in revulsion at the blitzing of Guernica by Hitler’s Condor Legion.

The primary image is conceived in the 1930s international style, but the print’s four subsidiary elements resound with a more specific familiarity. Each precisely parallels a prominent feature in Picasso’s greater and more complex lament for Guernica: a dying horse, a keening woman with a dead child across her lap, a corpse on the floor and (if I read Picasso right) falling classical columns.

Disappointingly, neither the wall caption nor the catalogue is helpful in explaining the relationship between this relatively obscure print and one of the world’s best-known paintings.

In the late 1930s, amid much in-fighting between factions of Mexico’s cultural left, Dosamantes joined other artists in forming a new print workshop, the Taller de Gráfica Popolar (TGP). Many members were followers of Siqueiros, such an arch-Stalinist that in 1940 he led a farcical machine-gun attack on the exiled Trotsky (who escaped by hiding under the bed), a few months before Ramón Mercader completed the job with his ice-pick.

Siqueiros proved more effective as propagandist than assassin. Thundering against “graphic expressions that correspond with official demagogy”, he encouraged the TGP to celebrate grassroots culture and socialist realism. Much of the studio’s output was predictably crude political satire – or what passed for satire in the eyes of Josef Stalin – and sometimes, indeed, corresponded quite closely with Soviet demagogy.

But TGP art also drew on more refined sources, as in the case of Leopoldo Méndez’s quasi-surreal lithographs and wood-engravings, and Isodoro Ocampo’s moving images of poverty, which seem to draw directly from New York artists of the Ashcan School.

Stylistic and ideological links between these Mexican artists and leftists on “the American scene” in the US were strong. Siqueiros and Orozco in particular spent time in New York (Rivera had served his apprenticeship in Europe) where they met artists working on the government’s Federal Art Project, and both Mexicans were significant influences on – to name one young American – Jackson Pollock. Cross-fertilisation between the artists of these two neighbouring American countries in the 1920s and 1930s is a powerful theme.

‘Revolution on Paper: Mexican Prints 1910-1960’, British Museum, London until April 5 2010. Tel: +44 (0)20 7 323 8299