Riddell graduated from the University of London in 1940, and served in the RAF Medical Service. He then worked at University College Hospital and at Massachussetts General hospital, Boston. On his return to Britain in 1955, he became lecturer, then reader, in surgery at the University of Manchester. In the early 1960s, he undertook important work in revising the clinical curriculum. In 1964 he was appointed to the chair of surgery at the University of Bristol.