Winstone was born in Hackney Hospital, London. He first lived in Caister Park Road Plaistow E13 and attended Portway infants and junior school. He moved to Enfield when he was seven, and grew up on a council estate just off the A10 road.  His father, Raymond J. Winstone (1933–2015), ran a fruit and vegetable business, while his mother, Margaret (née Richardson; 1932–1985), had a job emptying fruit machines. Winstone recalls playing with his friends on bomb sites (vacant lots with rubble from World War II bombs), until "Moors Murderers" Ian Brady and Myra Hindley were arrested for killing three children. Ray joined Brimsdown Primary School and then he was educated at Edmonton County School, which had changed from a grammar school to a comprehensive upon his arrival. He also attended Corona Theatre School. He did not take to school, eventually leaving with a single CSE (Grade 2) in Drama.