Martin graduated MB BCh BSc (Med) from the University of the Witwatersrand, Johannesburg. Shortly thereafter he left South Africa and after a few years of medical practice he joined the MRC Population Genetics Research Unit in Oxford. When the unit closed, he transferred to the Department of Genetics in Oxford as MRC External Staff, and as a Consultant to the Oxford Health Authority.
In 1981 he was appointed Professor of Human Genetics at he University off Amsterdam; then Prince Philip Professor of Paediatric Research at Guys Hospital London (1983) and Professor of Medical Genetics at the University of Cambridge (1995).
He has been awarded FRCPath, FRCP, and FRCPCH. Martin was a Founder Fellow of the Academy of Medical Sciences and was elected FRS in 2004.
Martin was a member of MRC Council (1988-1994) and a Governor of the Wellcome Trust (1996-2007). He was associated with the Muscular Dystrophy Campaign from 1980, and served as National Chairman from 1995-2011. Martin also chaired COMARE (the Committee on the Medical Aspects of Radiation in the Environment (1985-1992) and worked with other advisory committees. He served on the Nuffield Council of Bioethics from 1996-2003, and was Deputy Chair (2000-2003). He was a Non-Exececutive Director of Cambridge University Hospitals NHS Trust (2004-2014).