Sir William Arthian Davies (10 May 1901 - 19 September 1979) was a lawyer and judge in England and Wales.
William Arthian Davies was appointed a Justice of the Probate, Divorce and Admiralty Division of the High Court of England and Wales on 1 October 1952. He was knighted a few days later. He was transferred to the Queen's Bench Division on 3 April 1959. Sir William Arthian Davies was promoted to be a Lord Justice of Appeal in the Court of Appeal of England and Wales on 9 January 1961. Following that appointment, he was made a member of the Privy Council of the United Kingdom. He retired from his judicial office on 30 September 1974.