Cope was born in Erith in Kent (now in the London Borough of Bexley), where her father Fred Cope was manager of the local department store, Hedley Mitchell. She was educated at West Lodge Preparatory School in Sidcup and Farrington's School, Chislehurst, both in Kent. Following her graduation from St Hilda's College, Oxford Cope spent fifteen years as a primary-school teacher. In 1981, she became Arts and Reviews editor for the Inner London Education Authority magazine, "Contact". Five years later she became a freelance writer and was a television critic for "The Spectator" magazine until 1990.