Turner was born in 1948 in Wanstead, Essex, and grew up in London. He moved to Belfast in 1967 to study geography at Queen's University, and discovered one of his grandmothers was born on the Falls Road, qualifying him for an Irish passport. Around 1970 he began drawing cartoons for the Sunday News. After graduation he worked for the Belfast current affairs magazine Fortnight, and became its editor. In 1976 he was hired by The Irish Times as its political cartoonist. His work is syndicated to over 200 journals and newspapers around the world by the Cartoonists and Writers Syndicate.