Away from studying languages he was encouraged by family friend Cecil Harcourt-Smith (1859–1944), director of the Victoria and Albert Museum (1909–24) to develop an interest in the arts.
Cox started work as a volunteer at the National Gallery, London and then in the Department of Prints and Drawings at the British Museum.
He spent a short time at the Sorbonne which led to him writing a study of the French Renaissance painter Jehan Foucquet in 1931.
Cox is well known for the care and support he gave to museum staff, always remembering to send a note of congratulation to those responsible for a new exhibition or display.
In 1955 Cox was offered the post of Director and Secretary of the Victoria and Albert Museum by David Eccles, Minister of Eductation.
Cox acquired important objects such as the jade wine cup of the Shah Jahan and created a high standard of exhibitions, notably 'Opus Anglicanum' in 1963 and 'The Orange and the Rose' in 1964.