Was William Morris an anarchist? You might hardly think so looking at his chintzes and his willow-pattern wallpapers. But you only have to turn to News from Nowhere, his extraordinary utopian novel, to see how thoroughgoing an anarchist he was.

In this propaganda novel, first published in serial form in 1890 in the socialist newspaper the Commonweal, Morris depicts an England transformed by a revolution that had taken place in 1952. Previous structures of society have been overthrown. England has become a place of communistic freedom and genuine equality between men, women and children. There is no private property, no money, no divorce courts since laws of sexual ownership have been overthrown. Schools, prisons and central government are obsolete. When Tony Blair became prime minister and cited Morris as his hero, I think he had forgotten that in News from Nowhere the Houses of Parliament had become a dung-house, piled high with manure.

Morris's originality as visionary thinker lies in the case he makes for the centrality of art. He argued with ferocity that art was not a matter of pictures on the wall, not merely a plutocratic hobby. In his Nowhere, art is in the detail of everyday life, in the design of household goods, conservation of the countryside, thoughtful planning of towns, proper upkeep of roads. In this new post-revolutionary England, art is so omnipresent there is no need to define it. "What business have we with art at all unless all can share it?" By the 1880s – his violent years of involvement with socialist politics – Morris was prepared to die for the cause of democracy in art.

Daisy wallpaper by William Morris. Photograph: Historical Picture Archive/Corbis

Since I wrote Morris's biography, published 20 years ago, the chronological details of his life have come to seem less significant than the continuing spread of his ideas. The Anarchy & Beauty exhibition I have been curating for the National Portrait Gallery has given me the chance to assemble a cast of nearly 70 craftsmen and craftswomen, architects, designers, visual idealists and leftwing politicians, all of whom were touched by Morris's visionary thinking. All of them have had to pass a News from Nowhere test. Morris has exerted a powerful influence on thinking about art and design over the past century. He has been the constant niggle in the conscience. How can we combat all this luxury and waste?

What drove him into revolutionary activism was his anger and shame at the injustices within society. He burned with guilt at the fact that his "good fortune only" allowed him to live in beautiful surroundings and to pursue the work he adored. He fulminated that real art could not exist while people were divided into "cultivated and uncultivated classes". Often perilous experimental social mixes were a feature of the Morris-inspired arts and crafts communities as they developed in the late 19th and early 20th centuries, the Cotswolds being the favoured destination. Morris had invented a new species in society, the gentleman – and lady – artisan.

One of the star exhibits in the arts and crafts section of Anarchy & Beauty is Morris's own copy of the French edition of Karl Marx's Das Kapital handbound by TJ Cobden-Sanderson in a gold-tooled leather binding. Design extravagance? No, the ultimate example of Morris's conviction that perfectionism of design and craftsmanship should be available to everyone.

The most emotional passages in News from Nowhere are those about the natural beauty of the Earth. Morris saw how human beings depended on nature, noting the effect of the broad sweep and intimate detail of the landscape in lifting the spirits and contributing to psychological equilibrium. He viewed with desperation the speed with which Britain was becoming vulgarised and uglified. "Remember," he said (and how the comment resonates), "that rich men are not obliged to live in ugly houses, and yet they do."

Terence Conran sits in his Cone Chair. Photograph: Ray Williams

Garden cities developed in defiance of status-symbol architecture. The first of these was Letchworth, founded in 1903 by Ebenezer Howard. Garden cities were utopian in concept, aiming for "joyous union" of town and country. They were socially egalitarian. They were anti-snobbery and anti-luxury. They allowed space for the things that really mattered: the life of the mind and human creativity.

With their Voyseyesque white rough-cast architecture and their peasant-style cottage furniture from Heal's, garden-city dwellers could not avoid a certain sanctimoniousness. Bernard Shaw's cruel quip about cynical shopkeepers staining the simple life chest green and selling it to cottagers for 36 guineas still rings true in our own culture of spurious "craftsman-made" home furnishings and so-called "artisan baked" bread.

Morris, himself a craftsman of multiple skills, had watched with dismay the erosion of handcraftmanship in the ruthlessly exploitative industrial expansion of late-19th-century Britain. His "campaign against the age" in terms of loss of skills and of satisfying human occupation was taken up with renewed vigour in the years between the wars by the potter Bernard Leach, the handweaver Ethel Mairet and other idealistic craft practitioners.

The sculptor, letter-cutter and consummate type-designer Eric Gill was certainly the closest 20th-century counterpart to Morris both in the breadth of his creative skills and the fierceness of his critique of industrial society. To Gill, Morris was "that most manly of great man, as sensitive and passionate as he was fearless and hot-tempered". However, for Gill, fanatic Roman Catholic convert who even took to wearing the girdle of chastity, Morris, the Anglican priest-to-be turned atheist, made a fatal mistake in missing out on God.

Visions of Nowhere were still proving seductive in the mid-20th century. Many followers of Morris tried creating their own versions. The most thorough was at Dartington in Devon, an ambitious experiment in rural reconstruction started in 1925 by Dorothy Elmhirst and her husband Leonard, centred on a then-derelict 14th-century manor house near Totnes. The house was carefully restored following the principles that Morris first established in the Society for the Protection of Ancient Buildings. Workshops were opened, employing local labour. For this exhibition we are borrowing Elizabeth Peacock's great handwoven arts banner commissioned for the medieval hall – symbolic of the resurrection of art, craft and culture in the context of the rural community.

Garden Roller: 'Adam and Eve' by David Kindersley, designed by Eric Gill (1933). Photograph: Leeds Museums and Galleries

Visitors to Dartington frequently described it in Morrisian terms as an "earthly paradise". John Piper saw the large and slightly melancholy garden as the background for a whole succession of complicated love affairs. What a perfect setting for a utopian novel Dartington would make. The story of the place is full of gentle ironies, not least being the fact that the experiment was financed by Dorothy's inherited capitalist millions. Her father was William Collins Whitney, the American diplomat-tycoon.

My favourite section of the exhibition, and the one that I think is most full of surprises, is the Festival of Britain. At first sight, Morris and the festival might seem like a contradiction in terms. The 1951 South Bank exhibition was modernist in tenor, a paean to British technological achievement. Where is the aesthetic meeting point between Morris and the Skylon, unless one can find it in the soaring beauty of a gothicist church spire? The festival, to some extent, was an expression of the state socialism the anarchist in Morris so despised.

But there is still a strong element of News from Nowhere-thinking in the concept of the Festival of Britain. Back in the 1880s, Morris had looked forward to a rebirth of art as "the spontaneous expression of the pleasure of life innate in the whole people". It was now in the imaginative regeneration project of the postwar Labour government, in which art, architecture and design were of the essence, that Morris's ideals began to enter the political mainstream.

The South Bank exhibition was visited by 8.5 million people over the summer of 1951. This was art for the people on a considerable scale. And the parallels were emphasised by the fact that the fesival, like the final visionary scene in News from Nowhere, took place along the banks of the River Thames.

This was an era in which there were a myriad personal connections. For Labour party politicians in the early 1950s, Morris was still an almost living presence. Clement Attlee, the prime minister, acknowledged Morris as a major inspiration: it was the message of hope and transformation in News from Nowhere that had first made him a socialist. Attlee kept a framed print of GF Watt's well-known portrait of Morris hanging on his study wall.

Herbert Morrison, as president of council, held direct responsibility for the festival in Attlee's postwar administration. He, too, had potent links with Morris, having, as a young man, been a member of the Marxist revolutionary Social Democratic Federation, which Morris helped to form. Morrison had lived in Letchworth Garden City as a conscientious objector in the first world war, working as a market gardener, becoming a proficient folk dancer and marrying Daisy Kent, a handweaver and embroiderer he had met at the (teetotal) Skittles Inn in Letchworth. Morrison, known popularly as "Lord Festival", had a News from Nowhere background too.

Calyx furnishing fabric by Lucienne Day, 1951. Courtesy of the V&A, London. Photograph: James Stevenson

The South Bank exhibition took as its theme "Britain's contribution to civilisations – past, present and future". The director of architecture for the festival, Hugh Casson, gathered around him an exuberant team of almost 50 architect-designers to carry out the sequence of pavilions on the 11-hectare (27-acre) site. All the South Bank architects were under 45, trained but as yet inexperienced professionals. These were young idealists intent on the rebuilding of a new form of society after the destructiveness of war.

Postwar British modernism managed also to embrace the nation's ancient buildings. Acerbic critic Reyner Banham castigated "the so-called William Morris revival among leftwing architects", which he blamed for what he saw as the aesthetic pussy-footing of the Festival of Britain. The ravages of war had induced a newly solemn reassessment of the past. Casson was a modernist who lived with William Morris wallpaper. The William Morris Society was founded in 1955; the Victorian Society in 1958. The burgeoning conservation movement reflected Morris's own marvellous ferocity in defence of old buildings that he loved.

An unexpected champion of this period was the critic Herbert Read, defender of abstraction. Read is represented in Anarchy & Beauty by Patrick Heron's 1950 portrait from the National Portrait Gallery's collection, a painting miles away in its "contemporary" idiom from Morris's own pre‑Raphaelite world. But Read, too, had written a strange utopian novel, The Green Child. He had declared himself an anarchist in 1937. He respected Morris as a fellow member of that tribe.

Read recognised that, in his time, Morris was "as extreme as any modern artist". Morris the designer had been a revolutionary innovator whose influence on better standards of typography, furniture, textiles and craftsmanship had spread worldwide. Most crucially, Read said, it was Morris who had "rediscovered the artistic conscience, the most essential of all qualities in art".

Much of Morris's life was spent in anguish at his failure to solve the fundamental problem of making good design available to everyone. He was haunted by the suspicion that he was doing "nothing but make-believe", activity as useless as Louis XVI's lock-making, and deeply concerned that his own design and decorating business was simply "ministering to the swinish luxury of the rich".

Satchel owned by William Morris. Courtesy of the William Morris Gallery

This has been the challenge taken up by Terence Conran with his continuing mission to bring good design to the high street. As Conran put it recently: "I have a Morris-like view about not producing things only the rich can afford." We should not be deceived by Conran's image of self-satisfied tycoonery. He has for some years been consumed by Morris-style fury at the failure of successive governments to pay serious attention to design.

We still need Morris's colossal sense of anger, his talent for "bracing the nerves of the flaccid". How wonderful it was to see him spring back into action at the Venice Biennale in 2013 as the subject of a large-scale mural by the modern conceptual artist Jeremy Deller, past winner of the Turner prize. His mural We Sit Starving Amidst our Gold focuses on Morris as defender of socialist values against the venal power structures of the art world and ignorant commodification of the artwork. As Morris had expressed it back in the 19th century: "People who buy pictures also burn a lot of coal."

Deller's image shows Morris pent up with indignation, hurling Roman Abramovich's yacht into the Venice lagoon. It refers to an episode in 2011 when the Russian oligarch and art collector had anchored his yacht directly opposite the Biennale site, crassly blocking out the beauty of the view. It sets out to demonstrate the superior force of culture over business and money, and to show us that Morris's attitudes still matter.

Deller asks: "Will we know about Abramovich in 50 years time? We will certainly know about William Morris." We can still hear Morris's exasperated tones fulminating about the possession by the few of what should be the precious birthright of the many. Never has his viewpoint appeared more pertinent.

• Anarchy & Beauty: William Morris and His Legacy, 1860-1960 runs from 16 October to 11 January 2015 at the National Portrait Gallery, London WC2, npg.org.uk.