Pulsford was born in Staffordshire to Scottish parents. His family returned to Dunfermline when he was a child, and he subsequently attended Edinburgh College of Art (ECA) between 1933 and 1937. He, along with other prominent Scottish artists, embraced modernism and abstraction following the end of the war. Alan Davie, William Turnbull, William Gear and Eduardo Paolozzi are the key artists of the group with which he was association, and the National Galleries of Scotland regard Pulsford as the ‘fifth man’ of the group. Between 1952 and 1960 he taught at ECA and then at Canterbury College of Art.