Cohen studied at University College, Hull, where he obtained a BSc (external degree of the University of London) in 1954. He obtained his PhD in Zoology at the same institution (by then Hull University) in 1957. He went to the University of Birmingham for post-doctoral work, and was appointed Lecturer in the Department of Zoology and Comparative physiology in 1959. He worked for a year at Harvard Medical School then returned to Birmingham as a Senior Lecturer in 1968, a position he held until 1987. His former students include Sir Paul Nurse, winner of the 2001 Nobel Prize for Medicine. In 1974 the University of Birmingham awarded him a DSc for his work.