William Robert Withey was born in Redborough, Gloucestershire in 1915, the son of Robert Henry Withey (Engineer Lieutenant Commander, Royal Navy) and Mildred Mary Withey. William Withey joined the Royal Navy at the Britannia Royal Naval College in January 1928. He was appointed Midshipman (E) on 1 May 1932 and was appointed to the RN Engineering College, Keyham on 15 September 1932. He was promoted Sub Lieutenant (E) on 16 May 1935 and was appointed to the cruiser HMS ARETHUSA on 26 December 1936. He was promoted to Lieutenant (E) on 16 February 1937.

William Withey joined submarines on 24 April 1939 with an appointment to HMS DOLPHIN ‘for Submarine Training‘ and an appointment to the Submarine Depot Ship HMS FORTH ‘for Submarines‘ followed on 4 August 1939. He was then sent to Hong Kong with an appointment to the Submarine Depot Ship HMS MEDWAY ‘for Submarines‘ on 16 November 1939. The date of his appointment to HMS RAINBOW as Engineering Officer is yet to be established. RAINBOW conducted a number of War Patrols off Japan and in the area of the Dutch East Indies before being ordered to the Mediterranean. HMS RAINBOW sailed from Alexandria on 23 September 1940, and on 13 October she was ordered to leave her patrol area and return to Alexandria in the afternoon of 19 October, but she failed to arrive. It is now believed that HMS RAINBOW was accidentally rammed and sunk with all hands by the Italian M/V Antonietta Costa about 60 nautical miles East-North-East of Bari.

William Robert Withey was the husband of Phyllis May Withey (née Gordon), and he is commemorated on the Portsmouth Naval Memorial on Panel No. 37 Column No. 1.