Jones was born in Widnes, Cheshire, the third of four sons of Lieutenant Colonel Albert Jones. His father was the borough medical officer. Jones spent time in India as a child, where his brothers nicknamed him "Doolally Tap". He retained the nickname "Tap" for the rest of his life. After grammar school, he studied medicine at Liverpool University, where he met his future wife. His three brothers all became doctors, like their father, but Jones soon switched to veterinary science. He was a keen sportsman, representing the university and Lancashire at rugby union. He also enjoyed shooting and the outdoor life, but he showed little interest in his studies.
Edward joined the RAF in 1935. He trained as a pilot at Netheravon and joined "B" Flight of No. 17 Squadron in Kenley, flying Gauntlet fighters. In March 1937 the flight was detached to form No. 80 Squadron which flew the Gladiator, the RAF's last biplane fighter. As a pilot officer, he was its adjutant from May 1937. He also played rugby for the RAF. Promoted to flying officer, his squadron deployed to Egypt in April 1938. He became commander of "A" Flight of No. 80 Squadron in March 1940, while he was based in Amriya in Egypt.
After Italy declared war on the United Kingdom and France on 10 June 1940, Jones took charge of a flight armed with modern Hurricane fighters. He took charge of a flight of Gladiator when it moved to Trikala in central Greece in November 1940. He was in action within days, engaging a formation of more modern Fiat CR.42 fighters, also biplanes, of the Italian Regia Aeronautica to the north of Ioannina. He shot down one on 27 November, then two more the next day over Delvinakion, but was injured in the dogfight and spent a month recovering from a bullet wound in his neck. He returned to duty on 21 December, and took command of No. 80 Squadron on 27 December, after its commander, Squadron Leader Bill Hickey, was killed in action. Jones shot down two further Fiats on 28 February 1941, and was awarded an immediate Distinguished Flying Cross. He also received a Flying Cross from the Greek government. After leave in Egypt, Jones returned to No. 80 Squadron. It had been re-equipped with modern Hurricane fighters shortly before Germany invaded Greece on 6 April 1941. His battered squadron withdrew to Crete, then back to Egypt. Finally, it moved to RAF Aqir in Palestine to regroup, where it fought against the Vichy French in Syria. He left No. 80 Squadron in 1942, and was awarded the Distinguished Service Order. He spent a year with the Rhodesian Air Training Group, then took command of the RAF Hawkinge in Kent. After qualifying at the Army Staff College he was promoted to Acting Group Captain in May 1943, and joined the staff preparing tactical fighter operations for D-Day. His group, No. 83 Group, transferred to France shortly after D-Day, and moved eastwards with the front line. He stayed with the Group during the whole campaign in Northwest Europe as Group Captain Operations and being appointed an Officer of the Order of the British Empire in December 1944, when he returned to operational duties, taking command of No. 121 Wing with its four squadrons of Typhoon fighters, based at Volkel in the Netherlands. He was appointed a Commander of the Dutch Order of Orange-Nassau in 1945.