After his first solo exhibition in Johannesburg in 1920, Wolfe showed extensively in Britain and internationally. He provided the frontispiece to the twelfth and last of the Furnival Books (1930-32), John Collier's Green Thoughts, with a foreword by Osbert Sitwell. He exhibited at the Royal Academy from 1951 to 1970. He was elected an Associate Member of the Academy in 1967 and a Member in 1972.
His work is held by the Tate Gallery, the Royal Academy, the National Portrait Gallery, London and many other public and private collections including the Dixson Galleries, State Library of New South Wales, Sydney . In the National Portrait Gallery collection is a portrait of South African/British writer and poet William Plomer seated on a chair, in oils, dated 1929. The Dixson Galleries in Sydney holds one of his work which is a portrait of Randolph Hughes, Esq. (1889–1955) painted in 1932(?).