Captain Majendie was educated at Wellington College and Kings College, Cambridge. After service in the Royal Air Force during World War II, he joined the British Overseas Airways Corporation.
British Overseas Airways Corporation, often referred to as BOAC, was formed in 1939 as a merger of Imperial Airways and British Airways. During World War II the airline operated as directed by the Secretary of State for Air, initially as the transport service for the RAF, with no requirement to act commercially. The Civil Aviation Act 1946 set up the three airlines as corporations under public ownership and control, with BOAC operating the Commonwealth routes as well as the Far East and North America.
The Ministry of Supply ordered two de Havilland Comets in 1946 and BOAC joined them in making orders. Captain Majendie was appointed to special duties in relation to the Comet I aircraft in 1949 and started his service as Flight Captain of BOAC's Comet Fleet in 1951. In May 1951 BOAC borrowed and test flew one of the Ministry of Supply's Comets and on 2 May 1952 BOAC used the Comet G-ALYP to launch the World's first commercial passenger jet service, with Majendie at the helm. However, several air accidents hit the Comet fleet between 1952 and 1954. Majendie went onto navigate the first civil jet crossing of the South Atlantic during 1953.
In 1954 Captain Majendie left BOAC to take up a position at Smiths Industries Ltd and then served as the Managing Director of their Aviation Division between 1963 and 1967 and gained an international reputation as a designer of of automatic flight control systems. He later became Deputy Chairman of the Molins Oranization Ltd and Chairman of the Civil Air Transport Industry Training Board.