Farmer, a good amateur painter, was professionally a distinguished dentist. After attending Newcastle-under-Lyme High School, he read dentistry at Liverpool University from 1936 to 1941, followed by Second World War service as a Surgeon Lieutenant in the RNVR and a post-war period at Queen’s College, Cambridge (1948–1950: MA 1955). He was appointed Lecturer in Parodontal Diseases at Liverpool in 1950, its Louis Cohen Professor of Dental Surgery, 1957–1982 and from 1977 was also Dean of the Faculty of Medicine there. In the mid-1970s the university decided to establish an annual exhibition of artwork produced by staff and the fact that Professor Farmer opened the first such exhibition in June 1976 suggests he was probably instrumental in this. For ten years after his retirement in 1982 he was much involved with the charity Age Concern and was a member of its national executive committee, 1988–1992.