Robinson's father was a manufacturer of surgical dressings and one of the inventors of cotton wool. Robinson, who was born at Chesterfield in Derbyshire, was educated at the University of Manchester where he obtained a DSc in 1910. From 1912 to 1930 Robinson held chairs in organic chemistry successively at Sydney (1912–15), Liverpool (1915–20), St. Andrews (1921–22), Manchester (1922–28), and University College, London (1928–30). In 1930 he was appointed to the chair of chemistry at Oxford, a post he occupied until his retirement in 1955.

Early in his career, while working with William Perkin Jr. at Manchester, Robinson became interested in the natural dyes brazilin and hematoxylin. Important advances were achieved in understanding the chemistry of these compounds and their derivatives, which eventually led to his syntheses of anthocyanins and flavones, important plant pigments. Robinson also worked on the physiologically active alkaloids and established the structure of morphine (1925) and strychnine (1946). For his “investigations of plant products of biological importance, especially the alkaloids” Robinson was awarded the 1947 Nobel Prize for chemistry.

From 1945 to 1950, Robinson served as president of the Royal Society.