Turnbull was born in Dundee. He left school at 15 and worked as an illustrator on detective and romance stories for the local publishing house, DC Thompson, while studying art at evening classes. After serving as an RAF pilot in the Second World War, Turnbull studied at the Slade School of Art in London and lived in Paris from 1948 to 1950. His early sculptures were influenced by Surrealism and primitive art. Frequently made of bronze, they had worn, crusty surfaces. His bronzes of the mid- to late 1950s were tall and totemic in structure. Turnbull began to work with steel in the early 1960s as its strength allowed him to create more open forms and it could also be painted.