Dickson was born in Northwood, Middlesex, in September 1898 and was educated at Haileybury College. In 1916 he joined the Royal Naval Air Service, serving on the carrier "HMS Furious" before joining the (now independent) RAF in 1918.

He started his RAF career working as a test pilot before serving in the Air Ministry between 1923 and 1926. Subsequently he joined No 56 (Fighter) squadron (1926-27), attended the Royal Air Force Staff College, Andover (1927-28), served in India (1929-30), commanded RAF Station Hawkinge and No 25 (Fighter) Squadron (1935-36), and then acted as an instructor at Directing Staff at Andover (1936-38). In 1939 he attended the Imperial Defence College (1939), and was appointed Group Captain in 1940 and Air Commodore in 1941. He was Director of Plans, Air Ministry (1941-42), commanded Nos 9 and 10 Groups of Fighter Command (as an Air Vice Marshal) and No 83 Group (1943-44), and was then sent in 1944 to Italy to command the Desert Air Force. He returned in 1945 to serve as Assistant Chief of Air Staff.

After World War Two he was promoted Air Marshal and joined the Air Council (June 1946), serving as Commander-in-Chief Middle East (1948-50), Member for Supply and Organization, Air Council (1950-52), Chief of Air Staff (1953-56, becoming Marshal of the RAF in 1954), Chairman of the Chiefs of staff (1956-59), and Chief of the Defence Staff (1958-59).

He was appointed OBE in 1934, CB in 1942, CBE in 1945, KBE in 1946, KCB in 1952, and GCB in 1953. He died in September 1987.