Farquhar received his medical education at Birmingham, qualifying MB ChB there in 1938. After he obtained his Fellowship, he specialised in obstetrics and gynaecology, holding junior and registrar posts at the Birmingham Maternity Hospital and at the Birmingham and Midland Hospital for Women. Later he moved to Yorkshire and was surgeon to the Maternity Hospital at Leeds and to the Leeds Hospital for Women; he was also a consultant in surgery, gynaecology and obstetrics to the Leeds regional hospital board. He died on 7 February 1994.