Robinson was born in London, and attended Winchester College and Corpus Christi College, Oxford. He joined the staff of the Victoria and Albert Museum in 1939 and was shortly afterwards transferred to the Department of Metalwork where, apart from war service in the East from 1939 to 1946, he spent the rest of his career. He served as Keeper of the Department of Metalwork from 1966 until his retirement in 1972. In 1967 he was elected honorary president of the To-ken Society of Great Britain and was president of the Royal Asiatic Society from 1970 to 1973. He was a Fellow of the Society of Antiquaries and a Fellow of the British Academy. His principal fields of scholarship were: Persian miniature paintings (he developed the standard classification and chronology), Japanese swords, and the artist Utagawa Kuniyoshi (he established the artist's place among the great masters of ukiyo-e). He died in 2005. He had married twice: firstly Mary Stewart, who died in 1954, and secondly Oriel Steel, with whom he had a son and a daughter.

The Royal Asiatic Society of Great Britain and Ireland was founded by the eminent Sanskrit scholar Sir Henry Thomas Colebrooke on the 15th March 1823. It received its Royal Charter from King George IV on the 11th August 1824 'for the investigation of subjects connected with and for the encouragement of science, literature and the arts in relation to Asia'. It continues as a forum for those who are interested in the languages, cultures and history of Asia to meet and exchange ideas.