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. His work has appeared in numerous British publications including Punch, Lilliput, the Evening Standard, Evening News, The Guardian, The Spectator, The Independent, The Sunday Times, The Mail on Sunday, and Private Eye; all his work is signed simply as "HEATH". He has been cartoon editor of the Spectator since 1991 and the cartoons which are published have not always adhered to the magazine's conservative politics. Heath's own political cartoons have also appeared in the Independent.