Blackburn was born on 26 July 1918. He was the son of Brigadier Arthur Seaforth Blackburn VC and Rose Ada Blackburn (nee Kelly). His father was at that time a Commissioner of the now defunct Commonwealth Court of Conciliation and Arbitration. His father had previously been a prominent legal practitioner in South Australia. Blackburn was educated at St Peter's College, Adelaide, South Australia and was an undergraduate at St Mark's College at the University of Adelaide. He graduated with First Class Honours in English Literature from the University of Adelaide. He won the John Howard Clark Prize as the candidate who was placed highest in the final examination. He was chosen as the Rhodes Scholar for South Australia in 1940, but did not take it up immediately because of the outbreak of the Second World War.
During the Second World War, he enlisted with the Australian Army on 14 May 1940 at Adelaide. He served with the Australian Infantry Forces (AIF) in active service in North Africa and Papua New Guinea until his discharge on 7 November 1945 as a Captain in the 2/9 Division Cavalry Regiment.
At the end of the war, he took up his Rhodes Scholarship at Magdalen College. He and another South Australian, the Honourable Justice Andrew Wells, became the first ‘Dominion’ students to be awarded the Eldon Scholarship. As a result, he attended the Eldon Law School in 1949 and graduated with a Bachelor of Civil Law. Blackburn was called to the Bar in the United Kingdom in Inner Temple in 1949.
Blackburn returned to Australia after his Oxford studies. He was admitted as a legal practitioner in South Australia in 1951. He became a partner of the South Australian law firm Finlaysons. He left legal practice to take up an academic career in 1950. Between 1950 and 1957 he was appointed Bonython Professor of Law at the Adelaide University. He married his wife Bryony Helen Dutton in 1951. He became the Dean of the Faculty of Law in 1951 and served as Dean there until 1957. He continued as a member of the Faculty until 1965. His daughter and son were born whilst he was teaching at the Adelaide University.
In 1957 he was commissioned as a Lieutenant Colonel and given command of the Adelaide University Regiment. In 1962 he was commissioned as a Colonel and given command of the First Battalion of the Royal South Australian Regiment. He served there until 1965. He was made an OBE on 1 January 1965 in honour of his military service.
He left academic life and was appointed a judge of the Supreme Court of the Northern Territory in 1966. During this time, he became President of the Arts Council of the Northern Territory. It was during his judicial life in the Northern Territory that he decided the first significant case concerning Aboriginal Land Rights in Australia. This was the case of Milirrpum v. Nabalco in which important issues of aboriginal land rights were canvassed. In that case he held that the communal system in which Australian Aborigines had lived could be called a “government of law, and not of men”, accepting that was a system of law predating British settlement. However, he ruled that the British common law did not recognize communal interests and in any event, those interests were extinguished by the assertion of British sovereignty over the land in question. The case led to the eventual introduction of the Aboriginal Land Rights Act 1976.
In May 1971 he was appointed as a judge of the Supreme Court of the Australian Capital Territory. In that same year, he was also appointed a judge of the Federal Court of Australia in 1977 on that court's establishment and served as a judge in that latter court until 1984. He was appointed chief judge of Supreme Court on 7 November 1977. He was appointed chief justice on 7 May 1982 when that the position replaced the former position of chief judge.
He was the chairperson of the Law Reform Commission of the Australian Capital Territory from 1971 to 1976. In 1979, Blackburn authored a biographical entry in the Australian Dictionary of Biography about his father. In keeping with Blackburn's nature of not seeking honours, he failed to note in the entry that he had himself gone on to become a distinguished judge.
He was Patron of the St John Council for Australian Capital Territory from 1981 to 1984. In 1981, he became a Commander of the Order of St John of Jerusalem k honour of his service. He was knighted on 31 December 1982 for his services to the law. He became Chancellor of the Australian National University in 1984.
Blackburn retired as chief justice due to ill health on 31 March 1985. At his retirement ceremony, Mr J Faulks speaking on behalf of the legal profession said:
'Amongst the lessons we have learned from you, Chief Justice, is the importance of humanity and understanding in the practise of the law. These qualities have been demonstrated again and again during your time on the Bench. .... Your Honour has also shown us that excellence in knowledge and even in ability is nothing without true humanity and concern for others. Your Honour has shown in word and in example that humility and an appreciation of the other's point of view are the hallmarks of a good lawyer, whether he be judge, solicitor or barrister'
In 1986 he was elected an Hononary Fellow of St Mark's College. Blackburn was also invited to give the first Harrison Memorial Lecture at the Royal Military College at Duntroon after the Officer Training School was moved from Portsea. In May of that year, Blackburn was one of three former chief justices appointed by the Australian Government to be Parliamentary Commissioners in a Special Commission of Inquiry to investigate the conduct of Justice Lionel Murphy concerning allegations that Murphy had attempted to pervert the course of justice in the criminal proceeding involving solicitor Morgan Ryan. He was appointed notwithstanding his ill-health because of his skills and abilities. Whilst the inquiry did not proceed to conclusion because of Murphy's own illness and subsequent death, the commissioners did make a report on what constituted misconduct for a judge under the Australian Constitution. Blackburn concluded:
"'roved misbehaviour' means such misconduct, whether criminal or not, and whether or not displayed in the actual exercise of judicial functions, as, being morally wrong, demonstrates the unfitness for office of the judge in question."
Blackburn died on 1 October 1987.
In 1996, the Law Society of the Australian Capital Territory inaugurated the Sir Richard Blackburn lectures in honour of Blackburn's services to the legal community. The following persons have had the honour of giving the talk:
