Professor Murphy studied PPP at Oxford University and then undertook her clinical psychology training at the University of Birmingham, following which she was employed as a Clinical Psychologist at the Institute of Psychiatry, London completing her PhD there.
Since that time, she has worked at the Institute of Child Health and Great Ormond Street Hospital, London and was the academic director of the DClinPsy course at Lancaster University. She has worked at the Tizard Centre, University of Kent from 1993 - 2004 and 2006 to present, where she was Co-Director from 2012-2016.
Professor Murphy has taught on both the undergraduate and postgraduate courses at Tizard. She developed and convened the MSc in Analysis and Intervention in Learning Disabilities and has been instrumental in developing the MA Postgraduate studies in Intellectual and Developmental Disabilities and Forensic Issues.
She currently supervises PhD students most of whose research focuses on autism and learning disabilities and the criminal justice system.