Cropper studied acting at the Central School of Speech and Drama in London. She made her television debut as Chrysalis in The Insect Play (1960), based on the 1921 play by Czech brothers Josef and Karel Čapek. She appeared in Emergency Ward 10 three times and on Coronation Street three times in 1962. She came to prominence playing a young schizophrenic in the television play In Two Minds (The Wednesday Play, BBC, 1967) by David Mercer. which won the Writers' Guild Award for the Best Television Play of 1967.