Within a year of gaining his pilot's wings in 1934, Eveleigh was posted to No 802 Squadron of the Fleet Air Arm, at that time under the control of the RAF. After completing floatplane training and a concentrated period of deck landing practices at Gosport, Eveleigh joined Glorious, which was based with the Mediterranean Fleet at Malta. When not embarked, Eveleigh and his fellow pilots flew their agile Nimrod bi-plane fleet fighters from the airfield at Halfar on the south of the island.
The fleet carrier Glorious, launched in 1916 as a cruiser hull but converted and commissioned as an aircraft carrier in 1930, was in great demand during the annual Fleet exercises and there were few major ports in the Mediterranean that Eveleigh did not visit. This also placed heavy social demands on the young and eligible naval and RAF officers.
Eveleigh spent an unusually long time with No 802 and rose to become a flight commander. He returned to England just once when he flew a Nimrod in a formation flypast to celebrate the Coronation of King George VI in 1937. At the end of the following year, after almost four years with No 802, Eveleigh returned to Gosport as a deck-landing instructor.
The eldest of five boys - two died in action during the war - Geoffrey Charles Eveleigh was born on October 25 1912 at Henley-on-Thames and educated at Brighton College. Keen on flying from the moment he saw an aircraft make a forced landing in a water meadow near his home, Eveleigh gained entrance to the RAF College Cranwell as a flight cadet in January 1932. At Cranwell, Eveleigh excelled, and in addition to gaining his colours at soccer, swimming and athletics, he was awarded the Sword of Honour as the outstanding flight cadet of his entry.
He was rewarded with the highly sought-after posting to No 43 (Fighting Cocks) fighter squadron flying the elegant Hawker Fury. After a year with No 43, Eveleigh joined No 802.
In November 1939 Eveleigh moved to the RAF's signals establishment at Leighton Buzzard to specialise in wireless and signals, a discipline he would pursue for the rest of his time in the RAF. In January 1941 he joined the Bomber Development Unit at Boscombe Down investigating the use of radio beams, based on the German Lorenz system, as an aid to landing in bad weather.
Eveleigh spent most of the war on secret signals work at Headquarters Bomber Command. Great advances were made in blind bombing and navigation aids, and these provided the strategic bomber force with a level of accuracy that increased its effectiveness greatly. After being mentioned in dispatches in 1943, Eveleigh was appointed CBE in January 1945 in recognition of his wartime work.
After six months in south-east Asia in 1945, Eveleigh joined the RAF Delegation in Washington as the Director of Signals, a post he held for three years. At the end of 1951 he returned to Headquarters Bomber Command as the Chief Signals Officer, a period that coincided with the introduction of the RAF's first jet bomber and planning for the arrival of the first of the strategic nuclear V-bombers.
Eveleigh commanded the fighter airfield at North Weald in 1954 before embarking on a two-year appointment as the Assistant Chief of the Air Staff of the RNZAF. At this time, the New Zealanders made a significant contribution during the Malayan emergency, with fighter and transport squadrons involved in operations against the communist guerrillas.
After attending the Imperial Defence College in 1958, Eveleigh moved to the Air Ministry where he became the Director General of Signals (RAF). He arrived in the wake of the 1957 Sandys White Paper, which had a profound effect on the organisation and development of the RAF's air defence capability.
With the anticipated introduction into RAF service of supersonic fighters and surface-to-air missile defences, allied to the developing threat from a large Soviet bomber force and the advent of the ballistic missile, a major review of the UK's air defence and early warning system was necessary. Costs for taking account of Duncan Sandys's edicts, and the major review and amendments to current plans, escalated; the scientists recommended that military and civil air traffic control radars should also be combined and introduced into the wider scheme for air defence.
Eveleigh was at the centre of these complex discussions and negotiations and was chairman of numerous review groups. At one stage he had a celebrated disagreement with his immediate superior, the Vice Chief of the Air Staff, regarding the proposals for, and the sighting of, new early-warning radars and their associated control and reporting system. In the event, the decisions he took were accepted and a system was introduced that served the RAF until beyond the end of the Cold War.
In July 1961 Eveleigh moved to Fighter Command as the Air Officer Administration, spending the next three years preparing and implementing the introduction of the new air defence system. Some of the radar sites were established in remote areas of the UK, and Eveleigh paid close attention to the needs of the airmen who would be based at these locations, in particular the Shetlands.
During this appointment, Eveleigh also spent much time in liaison with the USAF, and with local authorities, planning the RAF's involvement for the introduction of the Ballistic Missile Early Warning System (BMEWS) at Fylingdales on the Yorkshire Moors. At the end of his appointment at HQ Fighter Command, he was appointed CB.
Eveleigh retired from the RAF in March 1965; he and his wife left for Majorca, where they built their own house and remained for the next 25 years. He was able to indulge his interests in sailing and bird-watching.
In July 2005 Eveleigh was reunited with the Nimrod aircraft he flew during his time with No 802 when he was invited as the guest of honour at a special event on the eve of the annual Flying Legends Air Show. The aircraft (serial S1581) had been restored to flying condition by the Duxford-based Fighter Collection, and is the only airworthy example of the type in the world.
Geoffrey Eveleigh died on December 23. He married, in June 1939, Anthea Fraser; she died in 1998. A son and a daughter survive him.