With the world aghast at the horrors of the Syrian civil war and the military coup d’état in Egypt, it is as well to remember just how often revolutions have turned to violence and how long the conflict can go on before some sort of stability is restored. Nowhere was this more so than in Mexico, where the popular uprising against the 35-year rule of President Porfirio Diaz in 1910 resulted in a decade-long civil war and the deaths of around a million, many from starvation and disease caused by the tide of conflict.

It also resulted in an outpouring of new and nationalist art, the subject of an enlightening new exhibition in the Royal Academy’s upper Sackler Wing Galleries. The war itself, it should be added, was too intense to allow much direct art. Instead, just as in the American Civil War, it was gruesome. Photographers such as the Mexican Manuel Ramos and the American Walter H Horne made their reputation out of the slaughter. Ramos tried to show the effect in views of the battered buildings. Horne made an income of out of selling the postcards of death (there is a particularly gruesome series of an execution of three men) to the American soldiers camped on the border and peering over the Rio Grande at the action.

Painting, as in the American Civil War, found it harder to cope with the cataclysm around, save for the crude works on copper or tiles in the manner of the Mexican miracle paintings. The show does include, however, two powerful paintings done early on in the conflict by Mexican artists. Francisco Goitia’s Zacatecas Landscape with Hanged Men II has all the ferocity of Goya with its image of a rotting body hanging from a tree in a bleached desert landscape that has its own deathly beauty, while Saturnino Herrán’s Woman from Tehuantepec is an extraordinary portrait done in the style of Velázquez and Manet but with a fierceness of stroke and directness of look that is positively unnerving. Goitia had volunteered to serve with the northern revolutionary leader, Pancho Villa, as an artist and saw for himself the brutality of war before Villa was assassinated in a government trap.

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The real spurt to art in Mexico came with the ending of the war and the establishment of a new Republic in 1920. In political terms the result – as so often – was a triumph of the forces of order over the more radical movement of the peasantry as romanticised in the figure of Emiliano Zapata. The bitterness of a betrayed revolution was to last far longer than the war itself, with Zapata becoming, not least to Hollywood, who cast Marlon Brando in the role, the image of martyred heroism.

Whether glorious in its end or otherwise, the revolution had put Mexico on the map. Artists flocked back to take advantage of the public art being commissioned by the new socialist government. At the same time, it attracted a host of writers – DH Lawrence and Malcolm Lowry chief among them – and artists from north of the border and across the Atlantic, all keen to participate in the brave new world of sponsored art and the bright and violent imagery of Mexico.

You can find some of the political art of the time bombastic in its acclamation of the virtues of a socialist state and sentimental in its promotion of the people as heroes of the nation, but you cannot deny the energy or the freshness of the painters involved. Even without the great murals that made their reputation, Diego Rivera, David Alfaro Siqueiros and José Orozco – known as “Los Tres Grandes”– impress you with the boldness and confidence of their vision of a country freed from oppression and rediscovering its Mayan and ancient roots.

In Dance in Tehuantepec (1928), Diego Rivera pictures his peasant dancers stately and proud, unflinching in their gaze and monumental in their pose as they move in line. Jose Clemente Orozco’s Barricade (1931) is an impassioned portrayal of human effort and exhaustion in the revolutionary effort. Siqueiros, who was to be imprisoned for his part in a failed attempt to assassinate Trotsky (Stalin’s agents fared better), presents Zapata in monumentalised terms, a face of supreme determination and moral dignity confined by the walls around him.

Not all Mexican artists took to this political culture but all, sensing the break from recent past, expressed a strong nationalism, seeking in the colours and people of the country a way to present an art that was special to the place. One of the strongest paintings in the exhibition is by Roberto Montenegro. Maya Women (1926) takes the profiles of ancient Mayan sculptural reliefs and re-creates them with the block colours of the post-impressionist painters he had studied in his years in France and Spain. The result is a picture of controlled energy that might seem Gauguinesque but is wholly different in its sense of sprung tension.

The other side of Mexican art at this period was the influx of artists from abroad. The list of photographers arriving for short or longer stays reads like a roll call of the prewar giants – Henri Cartier-Bresson, Edward Weston, Paul Strand, Laura Gilpin, Robert Capa and Martin Munkacsi. There were painters, too, including Leon Underwood and Edward Burra from Britain, Josef Albers, the German abstract painter who visited the country repeatedly after his emigration to the US, the American Philip Guston and the Canadian-born Henrietta Shore.

While the foreign photographers took some great shots of the country, its unremitting light and dramatic shadow, it is difficult to sense that their Mexican experience had huge effect on their style or understanding. What the visiting photographers did influence was the ambitions and confidence of a gifted young generation of Mexican photographers such as Manuel and Lola Alvarez Bravo and Agustin Jimenez.

The history of Mexican art of this time can be written in the loves and mutual learning of the artists – Edward Weston and Tina Modotti, the Bravos, Rufino Tamayo and María Izquierdo and, of course, Frida Kahlo and Diego Rivera (although such is the correctness of our time that the caption for Frida Kahlo’s picture in the show determinedly does not mention the relationship now that she has become such a feminist figure in her own right). The women come out as equal to the men, even if they learned at first from their partners before splitting up and developing on their own. The street shots of Lola Alvarez Bravo, who decided to become a professional photographer after separating from her husband, are wonders of care and feeling. So too with the Italian model Tina Modotti, who became a role model for a new generation before being expelled for her political views in 1930 (she returned in 1939 under an assumed name after fighting in the Spanish Civil War).

When it comes to painting, the effect that Mexico had on its visitors seems to have been particularly profound. Josef Albers took hundreds of photographs of buildings and landscapes during his successive visits, carefully ordering them into patterns as the basis for his abstract works named after the Mayan places he saw. Edward Burra, who stayed with the increasingly alcoholic Malcolm Lowry at Cuernavaca, responded eagerly to the colour and the macabre of the country. His two watercolour and gouache pictures on show, Mexican Church (c1936) and El Paseo (c1938), serve as an answer to Evelyn Waugh’s characterization in Brideshead Revisited of the English artist returning from Latin America filled with its colour but too polite for its violent energy.

The Royal Academy’s moderately sized exhibition is too broad a brush to give much depth to its survey of Mexican art of the time. For that it needed to have decided whether to concentrate on Mexican art in its own right or the work of visiting foreign artists, rather than both. But as an introduction to a cultural outpouring too often ignored in this country, it is full of revelations, not least for demonstrating what state commissions can do in fostering a flowering of talent. If only a British government seemingly bent on starving the publicly supported arts to extinction could learn the lesson. But then, the Mexican government of the 1920s and 1930s actually believed art was important to the country and its people.

Mexico: a Revolution in Art, 1910-1940, Royal Academy of Arts, London W1 (020 7300 8000) to 29 September