Jellett was appointed assistant civil engineer to the Admiralty on 22 June 1933. He served in the Royal Navy Volunteer Reserve during the Second World War and was commissioned as a Temporary Captain. His engineering talents were called upon during the Invasion of Normandy where he was made Superintending Civil Engineer of Mulberry Harbour B, a temporary concrete harbour built at Arromanches.
Mulberry B was in use for five months following the invasion and landed two million men, half a million vehicles and four million tons of supplies for the Liberation of Europe.
In recognition of Jellett"s work with the Mulberry harbour he was appointed an Officer of the Order of the British Empire (military division) on 28 November 1944. His citation in the London Gazette referred to his "distinguished service in operations which led to the successful landing of allied forces in Normandy".
After the war from October 1945 to February 1946 he was Superintending Civil Engineer, Her Majesty Dockyard, Chatham. From 1946-1948 he was Deputy Docks Engineer, Southern Railway, Southampton Docks.
After nationalisation of the railway companies he was Docks Engineer, Southampton Docks, British Transport Commission from 1948-1958 and he was Chief Docks Engineer, Southampton Docks from 1958 until his retirement in 1966.
He also acted as an occasional advisor within the Engineer and Railway Staff Corps, he was promoted to Major of that corps on 3 July 1957. Jellett served as President of the Institution of Civil Engineers from November 1968 to November 1969. He authored the Harbours and Sea Works article entry in Encyclopaedia Britannica.
He lived in Southampton in Hampshire, from 1946 until his death in 1971.