MB ChB Sheffield 1961; FRCS Eng 1966.
Markham was born in Dewsbury, Yorkshire in May 1936. He was educated at Batley Grammar School and Sheffield University. Markham held a number of appointments at Sheffield Royal Hospital and Sheffield University, from 1965 specialising in orthopaedics. In 1972, Markham was appointed lecturer in orthopaedic surgery at the University Department of Orthopaedics at Sheffield Royal Infirmary. He was later appointed consultant orthopaedic surgeon to MRI and honorary clinical lecturer in orthopaedics at the University of Manchester. Markham was vice-president of the Medical Defence Union and a fellow of the British Orthopaedic Association.