Venner received his medical education at Adelaide University, where he qualified MB BS in 1946. He gained the Melbourne MS in 1951. After qualification, Venner was resident medical officer at the Royal Adelaide Hospital before serving as a captain with the Australian Army Medical Corps from 1947 to 1949. He was thereafter surgical registrar at the Royal Melbourne Hospital from 1950 to 1951 and senior surgical registrar in 1951. Coming to Britain, he was a surgical registrar at Hammersmith Hospital from 1952 to 1953 and gained his Fellowship during this period. Returning to Australia thereafter he was tutor in surgery and applied anatomy at the University of Adelaide from 1956 to 1963, honorary assistant surgeon to the Royal Adelaide Hospital from 1956 to 1964, honorary surgeon 1964 to 1970 and visiting surgeon from 1971. His death was reported to the College by his son in a letter dated 27 May 1991 as having occurred in April 1991.