Sayers, an only child, was born on 13 June 1893 at the Headmaster's House on Brewer Street in Oxford. She was the daughter of Helen Mary Leigh and her husband, the Rev. Henry Sayers. Her mother was a daughter of Frederick Leigh, a solicitor whose family roots were in the landed gentry in the Isle of Wight, and had been born at The Chestnuts, Millbrook, Hampshire. Her father, originally from Littlehampton, West Sussex, was a chaplain of Christ Church Cathedral, Oxford, and headmaster of Christ Church Cathedral School.