Richard Bennett topped the University of Adelaide medicine class of 1953 and followed this success with surgical training in Adelaide, Glasgow, and Leeds. At the age of 34 he was appointed Foundation Professor of Surgery at St Vincent's Hospital within the University of Melbourne, a position he held for 25 years. During this time he became recognised as a leader in the surgical management of breast cancer.
Professor Bennett has been heavily involved in the activities of the Peter MacCallum Cancer Institute, the Anti-Cancer Council of Victoria, and the Royal Australasian College of Surgeons. He has served the College in senior roles and established a foundation to promote surgical education and research.
In retirement he continued his association with the college, as its Executive Director for Surgical Affairs, through its program to provide tertiary medical services to Pacific Island nations, and in the establishment of Surgeons International, a foundation to support the education and training of medical personnel from under-privileged backgrounds.