Parry has a Bachelor of Science (1963) and a Doctor of Science (1982) from the University of London and a Doctor of Philosophy (1966) from King's College London. He was a postdoctoral fellow in the Protein Chemistry division at the Commonwealth Scientific and Industrial Research Organisation in Melbourne, Australia from 1966 to 1969. From 1969 to 1971 he worked for the Children's Cancer Research Foundation in Boston, Massachusetts. Later he became a research scientist at the Laboratory of Molecular Biophysics at Oxford University from 1971 to 1973. He then worked for many years on the faculty of Massey University.