He first saw action during World War I as a gunnery officer aboard HMS Southampton,[1] later taking part in the Battle of Jutland in 1916.

During the Second World War he was awarded the DSO after Operation Archery a raid on the Norwegian islands of Vågsøy and Måløy on 27 December 1941 in which nine enemy ships were sunk by the Navy and Royal Air Force and the garrisons were wiped out by the raiding force.

After becoming Flag Officer Commanding Gibraltar and Mediterranean Approaches in September 1943, Burrough succeeded Admiral Sir Bertram Ramsay as Allied Naval Commander-in-Chief, Expeditionary Force (ANXF), following Ramsay's death after an aircraft accident in January 1945.

[2][1] Planning the Allied naval strategy and operations, working closely with U.S. General Dwight D. Eisenhower during the final years of the war, Burrough was one of the signatories to the German Surrender Documents on 7 May 1945 at Rheims, France.

He remained as naval commander occupying post-war Germany, where among his duties he authorised the formation of the German Mine Sweeping Administration.