Born at Johannesburg, South Africa, Wolfe came to England and studied at the Slade School between 1916–18. Whilst at the Slade he was invited by Nina Hamnett to join Roger Fry’s Omega Workshops, with whom he first exhibited in 1918. He travelled extensively, particularly in France and was an early admirer of Matisse, who greatly influenced his work. Wolfe becoming known as "The English Matisse". In the early 1930s he designed sets for C B Cochran. He exhibited in Britain and abroad throughout his career both mixed and one-man exhibitions and was elected R.A. in 1972. There was an Arts Council retrospective in 1967. The Tate Gallery and many other public galleries hold examples of Wolfe’s work.