With its boundless optimism about the transformative potential of science, the Festival of Britain was the atomic age brought to the South Bank. This is more than a metaphor; scientific accuracy was woven, quite literally, into the very fabric of the buildings. As a fascinating new exhibition at the Wellcome Collection shows, many of the festival’s distinctive furnishings and wallpapers were the result of a characteristically Fifties collaboration between designers and some of the leading scientists of the day.

The Cambridge physicist Helen Megaw led this project to bring the microscopic beauty of crystalline structures into the aesthetic and commercial world of dresses, ties and carpets. “I am constantly being impressed by the beauty that crops up,” she wrote in 1946 of her work probing the structure of molecules through X-ray crystallography. “I would like to suggest not merely that designers should look through it for new ideas, but that they should select a few of the best which would be utilisable without substantial alteration, apply them to appropriate fabrics, and give such pattern its correct name.”

This is exactly what happened in 1951. Megaw had applied the principle herself with an embroidered cushion as a wedding present for her friend and colleague, Dorothy Hodgkin. In 1949 Mark Hartland Thomas, of the Council of Industrial Design, saw some of Megaw’s patterns at a lecture and created the Festival Pattern Group to put the plan into operation. By 1951 80 designs had been produced by no fewer than 28 companies.

The results are impressive. We see Hodgkin’s original diagram of the structure of insulin 8.27 turned into handsome wallpaper for the Regatta restaurant, delicate rosettes surrounded by powerful Matisse-like lines. The same molecule appears quite differently on a plastic laminate, an elegant filigree in blue and gold, roses emerging from a tangle of thorns.

Horse blood provides the structure for some lively amoeba-like dress patterns. Boric acid becomes suitably stark and angular wallpaper. Nylon produces the most recognisably molecular designs, a classic lattice of balls connected by rods. But even on furniture fabrics, exactness must be observed; the colour of the balls and the thickness of the rods correspond strictly with the types of atom and the strength of their bonds.

Such accuracy came from the scientific drawings arranged by Megaw from some of the leaders of the field, mainly based, like her, at the Cavendish Laboratory in Cambridge. These included Lawrence Bragg, who had won the Nobel prize for his work on X-rays which made the discovery of crystalline patterns possible, as well as Max Perutz, John Kendew and Hodgkin, all of whom went on to win Nobel prizes in the 1960s.

Their names, however, were kept secret at the time, seemingly to separate the project from their serious work. All the scientists did, though, receive £5 — except Hodgkin, who refused, saying: “I feel rather doubtful whether I own any copyright of a pattern pepetrated by nature.” Megaw supervised the production process, vetoing designs she felt were scientifically meaningless.

Fittingly, it is the mineral afwillite, Magew’s own specialism, which produces the most intriguing patterns. They wind across wallpaper like contour maps of Mars, or fly across brightly coloured dress fabrics like wobbly spaceships.

Even the most sceptical manufacturers were won over. “I must say that the design came out much better than I anticipated,” said one W. A. Dickie, a textile maker. “They strike an air of novelty and yet contain a unity which is mentally even more than visually perceived. I suppose that, in a way, was the underlying idea.”

Some of the patterns proved commercially successful, like glass patterned with Apophyllite 8.30. The ties apparently remained very popular. But the dresses were for one season only and the era’s scarcity discouraged manufacturers from taking risks on the rest.

One well-worn carpet is on display, salvaged by the crystallographer Gordon Cox for his office in Leeds, but most of the designs have languished for decades in the vaults of the Victoria & Albert and the exhibition is the first time they have been seen together since the festival. Simply presented, and accompanied by a glorious full-colour Central Information Office film of tie-wearing crowds disporting themselves by the Skylon, From Atoms to Patterns recaptures some of the spirit of that heady yet serious-minded moment.

From Atoms to Patterns: Crystal Structure Designs from the 1951 Festival of Britain, Wellcome Collection, Euston Road London NW1, until August 10. Admission free