Leigh was born Vivian Mary Hartley on 5 November 1913 in British India on the campus of St. Paul's School in Darjeeling, Bengal Presidency. She was the only child of Ernest Richard Hartley, a British broker, and his wife, Gertrude Mary Frances (née Yackjee; she also used her mother's maiden name of Robinson). Her father was born in Scotland in 1882, while her mother, a devout Roman Catholic, was born in Darjeeling in 1888 and may have been of Irish and either Armenian or Indian ancestry. Gertrude's parents, who lived in India, were Michael John Yackjee (born 1840), an Anglo-Indian man of independent means, and Mary Teresa Robinson (born 1856), who was born to an Irish family killed during the Indian Rebellion of 1857 and grew up in an orphanage, where she met Yackjee; they married in 1872 and had five children, of whom Gertrude was the youngest. Ernest and Gertrude Hartley were married in 1912 in Kensington, London.