Neave was educated at Eton College and Merton College, Oxford, trained as a lawyer, and became an officer in the British army at the beginning of World War II. Taken prisoner by the Germans, he became the first British officer to escape from the high-security PoW camp at Colditz. He was later recruited as an intelligence agent, and wrote several books about his war experiences.
Neave became a member of parliament in 1951, but his career was held back by a heart attack he suffered in 1959. Said to have master-minded Margaret Thatcher's campaign for the Conservative Party leadership in 1975, Neave was rewarded with the post of head of her private office. He was then appointed shadow Secretary of State for Northern Ireland and was poised to attain the equivalent Cabinet position. He was killed a few weeks before the general election which brought Thatcher to power as prime minister.