BM BCh Oxford 1943; FRCP 1963.
Matthews gained his medical education at University College Oxford and held resident appointments in Oxford. In 1949 Matthews came to MRI as chief assistant to the neurological unit, and from 1952 to 1954 was senior registrar in neurology at King's College Hospital. He was then consultant neurologist at Derbyshire Royal Infirmary before being appointed consultant physician with special interest in neurology at MRI and Crumpsall Hospital Manchester in 1968. By 1980, Matthews was professor of clinical neurology at Oxford University. He was also editor in chief of Journal of Neurological Science and a member of the Association of British Neurologists and of the Association of Physicians of Great Britain and Ireland.