Day was educated at the High Wycombe Technical Institute and the High Wycombe School of Art before being awarded a scholarship to the Royal College of Art in 1934. This was 'a great let down', as at that time there was little tuition in industrial design; he had to educate himself in modern design, using resources such as the Victoria & Albert Museum.

Day married Lucienne Conradi in 1942, two years after they had met at college. They spent much of the war teaching, and it was not until afterwards that their careers in design began to advance. Through a teaching colleague, Peter Moro of the Design Research Unit, Robin Day became involved with exhibition design, early projects including Ministry of Supply exhibitions on the jet and British scientific instruments.

Robin continued in this field until the 1960s, but in 1948 a new career path - one closer to his ambitions - opened when he collaborated with colleague Clive Latimer on an entry for the Low Cost Furniture Competition, winning with a set of wall-mounted storage units. This success led to the couple's association with the furniture company Hille in 1949. The popular Hillestak chair, made from moulded plywood, followed the next year. The company was not used to the new medium, and perhaps Robin's experience in making moulded furniture for his flat during the war helped him guide them.

Day's flexibility as a designer was drawn upon for the 1951 Festival of Britain, for which he played the roles of product designer, graphic designer and exhibition designer.

Day has continued to design contemporary furniture for Hille and others, sometimes collaborating on projects with his wife. His work includes the 'Toro' seat used in London Underground stations, his televisions for Pye and his interiors for BOAC aeroplanes as well as numerous furniture designs.