Quick was born in London, England. She grew up in Dartford, Kent, the third of four children. She was educated at Dartford Grammar School for Girls, Kent. She was greatly aided by her English Teacher who encouraged her to pursue acting. She became a member of an amateur dramatic society in Crayford, Kent, while at school as well as appearing in many school productions. On leaving school, she went on in 1964 to pursue further studies at Lady Margaret Hall, Oxford. Quick was the first female President of the Oxford University Dramatic Society.