Windsor was born in Shoreditch, London, in 1937 (her birth was registered in Stepney), the only child of John Deeks, a costermonger, and his wife, Rose (née Ellis), a dressmaker. The family lived in Angela Street. Windsor is of English and Irish ancestry. In 1939 the family went to live with relatives in Yoakley Road, Stoke Newington, where Windsor attended St Mary's Infants' School in nearby Lordship Road. She was evacuated to Blackpool during the war. On her return in 1944 she attended William Patten School in Church Street. After the war she passed her 11-plus exams and earned a scholarship for a place at Our Lady's Convent in Stamford Hill. Her mother paid for her to have elocution lessons, and she trained at the Aida Foster School in Golders Green, making her stage debut at 13 and her West End debut in 1952 in the chorus of the musical Love From Judy which ran for two years. She took the stage name Windsor in 1953, inspired by the Coronation of Queen Elizabeth II. Television work soon poured in with her first series of Dreamer's Highway, The Jack Jackson Show and Six-Five Special.