William Davis was born in Simla, Punjab, India, in October 1901, the elder son of Walter Stewart Davis, of the Indian political service. He was educated at Summer Fields School, Oxford, and then the Royal Naval College at Osborne, Isle of Wight, and Dartmouth College.

He first served as a midshipman on HMS Neptune (September 1917-February 1919), and was promoted at various stages of his career before being made Commander in 1935. He served in the Tactical Staff Division at the Admiralty, 1936-37, then became Fleet Torpedo Officer and Staff Officer, Plans, to the Commander-in-Chief, Home Fleet, in 1938 before being appointed second in command and Executive Officer of HMS Hood in January 1939. He served on Hood until August 1940.

Promoted captain in December 1940, Davis returned to the Admiralty, first to the Planning Staff, then as Deputy Director of Operations Division Foreign in 1941, then from August of that year until March 1943 as Deputy Director of Plans. He was for a time seconded to the staff of Admiral of the Fleet Sir Roger Keyes, director of combined operations. From March 1943 to September 1944 he was given command of the cruiser HMS Mauritius, playing a role in the Allied landings in Sicily and Salerno, and also in the D-Day landings, before returning to the Admiralty.

After World War Two Davis was appointed Director of the Admiralty's Underwater Weapons Division and then he became Chief of Staff to the Commander-in-Chief, Home Fleet (1948–9). He was promoted to Rear-Admiral in 1950 and served as Naval Secretary to the Admiralty. From 1952 to 1954 he was flag officer, second in command, Mediterranean Fleet, when 1st Lord Mountbatten of Burma was commander-in-chief. He was appointed as Vice Chief of the Naval Staff in 1954 and (as a full Admiral) served as Commander-in-Chief, Home Fleet, and NATO Commander-in-Chief in the eastern Atlantic from 1958-60

He was appointed CB in 1952, KCB in 1956, and GCB in 1959.

He retired in 1960 and died in October 1987.