Morgan was born near Crowborough, East Sussex, in 1985. Her father is a wine broker and her mother held various positions as a nurse, gundog trainer and air stewardess. Morgan was educated at Cumnor House School, Danehill, East Sussex. "Having been chucked out of school in England, Sophie was sent to Gordonstoun School" in Moray, Scotland.
Morgan was left paralysed from the chest down after a road accident when she was 18 years old.
Prior to the accident, Morgan had planned to study Law at the University of Manchester. Having returned to live with her parents in Brighton, she instead opted to study art at the City College Brighton & Hove After completing her art foundation course, she started a bachelor of arts degree in fine arts at Goldsmiths, University of London. She later obtained a diploma in arts therapy from the Institute for Arts in Therapy and Education.