William Brooker studied at Croydon School of Art (1936-1939), Chelsea School of Art (1947-1949) and Goldsmiths College of Art (1948-1949). Between 1949 and 1965 he taught at a number of schools and academies including Bath, Wimbledon, Willesden and Harrow. In 1965 he was appointed as a senior lecturer at Central School of Arts and Crafts, London and from 1969 until 1981 he was Principal of the Wimbledon School of Art. Brooker had his first solo exhibition in 1955 at Arthur Tooth and Sons, where he continued to exhibit regularly. He also showed at the Royal Academy, the Leicester Gallery, and Agnew's in London. In 1968 his travels took him to America and Zambia, where he exhibited with William Scott in a show organised by the British Council.