William was educated at the Model School and attended night classes in art at the Technical School, taught by Kathleen Bridle. In 1928 he went on to Belfast College of Art, and in 1931 he won a scholarship to the Royal Academy Schools in London. There he won a silver medal and became a Landseer scholar in painting. In London he shared rooms with, the painters Alfred Janes and Mervyn Levy and the poet Dylan Thomas. He was awarded a Leverhulme scholarship in 1935.
Scott represented Britain in 1958 at the Venice Biennale. He exhibited at the Hanover Gallery in London, at the Martha Jackson Gallery in New York, Italy, Switzerland, West Germany, France, the Kasahara Gallery in Japan, Canada and Australia, as well as Belfast and Dublin. Retrospectives of his work were held at the Tate Gallery, London in 1972, in Edinburgh, Dublin and Belfast in 1986, by the Irish Museum of Modern Art, Dublin in 1998 and the Jerwood Gallery in 2013.