Heath was born on 13 October 1935, in Bloomsbury, London. His father, George Heath, was also a cartoonist of boy's adventure comics, a job he detested. Heath's relationship with both his parents was distant and neither birthdays nor Christmas were celebrated. During the war Heath was evacuated to his grandmother's house in Torcross, in Devon. In 1947 the family moved to Brighton. While studying at art college, which he loathed, Heath sold his first cartoons to "Melody Maker" for two guineas. He later got work illustrating album covers for Decca Records and drew a strip called "Nelly Know-all" for the "Women's Sunday Mirror". By the 1960s he was part of the Soho social crowd that included Jeffrey Bernard, Lucian Freud and Francis Bacon.