In a bold poster by the Beggarstaff brothers, Don Quixote looks resolute as he prepares to tilt his lance. This daringly simplified design advertised a show at the Lyceum Theatre in 1895. But it also summarises the defiant spirit underlying the arts and crafts movement, surveyed in a new epic show at the Victoria & Albert Museum.

Like Don Quixote, the men and women behind this ardent, angry and high-minded movement were determined to protest and attack. They deplored the cynical exploitation and alienation of workers in a machine-dominated world. William Morris, its most militant and messianic advocate, vowed to do battle "against the age". Both he and John Ruskin condemned the ruthlessness, monotony and rampant pollution fouling the late 19th-century world. Calling for a return to sensuous, hand-made production, they wanted craftsmen to be given a far higher status within society. Ruskin in particular hoped that the old hierarchical divisions between gentlemen and artisans would melt away, replaced by a brave new order.

It was an enterprise as doomed as Don Quixote's gallant yet absurd adventures. High ideals led inexorably to crisis. Handmade objects cost so much to execute, compared with mechanised mass production, that only the wealthy could afford them. So the elevated arts and crafts vision of transforming everyone's home into a work of art was negated by a remorseless economic reality. Only five years after C R Ashbee took the Guild and School of Handicraft out of London's East End slums, rehousing it in the sequestered Cotswolds beauty of Chipping Campden, it ended in financial calamity.

The most outstanding exhibits at the V&A turn out, time and again, to be commissioned by privileged clients. But the contradictions inherent in the endeavour should not prevent us from savouring its finest achievements. The movement won an extensive international following, not least in the US, where Frank Lloyd Wright and others were impressed by native Americans' ability to live in harmony with nature. Chicago became the home of the far-reaching Prairie School, while the aptly named Byrdcliffe Colony flourished as an arts and crafts community. Lloyd Wright is outstanding here, as he invests even an object as modest as a "triplicate" vase with the severe monumentality of a primordial temple.

In Japan, a country whose artists had inspired so many avant-garde painters throughout Europe in the 19th century, influence started going the other way with the arts-and-crafts-inspired Mingei movement. Fascinated by historic folk crafts, its members amassed a superb collection of old, paint-splashed vases, as well as implements and garments as unpredictable as a kettle-hanger, a back protector and a sledge-hauling jacket.

Mingei brought about a new style of middle-class living, culminating in an extraordinary house known as the Mikuniso, which was intended to reveal how the Japanese could enjoy both indigenous and western styles in their domestic interiors. Designed by Yanagi Soetsu, Hamada Shoji and Kawai Kanjiro, leaders of the Mingei group, it became the guest house for the Yamamoto family home. After the Second World War, it was believed to have been destroyed. However, it was rediscovered a few years ago by the architectural historian Dr Kawashima, who has acted as consultant on an ambitious reconstruction of the interior in the V&A exhibition.

The result is fascinating. We can see how well the western-style dining room, with its high-backed chairs, chimes in with a Japanese-style reception room, where everything is low-slung and reliant on rugs and matting. Both spaces are marked by extreme simplicity. Everything has been pared down to primary forms. In this crucial respect, the arts and crafts exponents had a potent, lasting influence on the development of the modern movement at its most elemental.

Not everything on show, however, is stripped of all extraneous matter. In Scotland, Charles Rennie Mackintosh reached the quintessence of austerity with his stark, puritanical chair designed for a house called, bracingly, Windyhill. But his wife, Margaret Macdonald Mackintosh, was not afraid to indulge in decorative elaboration with a startling pair of embroidered panels, where bloodless and elongated women close their eyes and lean towards each other like phantoms haunting a funeral ceremony.

Her remarkable contemporary, Phoebe Traquair, went even further in the direction of heightened spirituality and ornamental richness. Executed between 1895 and 1902, her four embroidered linen panels, The Progress of a Soul, prophesy the even greater decorative splendour explored by Gustav Klimt, whose most celebrated painting focuses, as Traquair's does, on a kiss where spirituality and eroticism meet in a fervent union.

By the time we reach Ninian Comper's sumptuous cope and hood, embroidered in silk damask, the starkness of Mackintosh's oak chair may seem very remote. And yet the arts and crafts movement refused to limit itself. It believed that there was room for severe, Shaker-like furniture as well as the outrageous ostentation of a colossal, wool pile carpet, such as the one designed by Richard Riemerschmid in 1903 for the house of Karl Thieme in Munich.

Here, the entire surface seems to have been splashed with gouts of blood. It must have made the room look disconcertingly like the scene of a crime. But Riemerschmid derived his design from highly stylised floral motifs, reminding us that, even at its most provocative, the arts and crafts movement always found redemptive inspiration in the natural world.

"International Arts and Crafts" is at the Victoria & Albert Museum, London SW7 (0870 906 3883) until 24 July