At the beginning of World War II her father, a member of the Territorial Army, was mobilised, and Riley, together with her mother and sister Sally, moved to a cottage in Cornwall. The cottage, not far from the sea near Padstow, was shared with an aunt who was a former student at Goldsmiths' College, London. Primary education came in the form of irregular talks and lectures by non-qualified or retired teachers. She attended Cheltenham Ladies' College (1946–1948) and then studied art at Goldsmiths' College (1949–52), and later at the Royal College of Art (1952–55).