Educated at Eton College and Royal Military Academy Sandhurst, Legge-Bourke was commissioned into the Royal Horse Guards in 1934. He served there throughout World War II, rising to the rank of major. In 1941, he was liaison officer, GHQ, British Forces in Greece and served with the 7th Armoured Division at El Alamein.
Legge-Bourke was elected member of Parliament for Isle of Ely in 1945 as a member of the Conservative Party. His gain from the Liberal James A. de Rothschild was the only Conservative gain of the election. Legge-Bourke was prominent as a chairman of the 1922 Committee of Conservative backbenchers. In 1960 he was invested as a KBE. As an East Anglian representative, he was particularly interested in land drainage and was vice-President of the Association of Drainage Authorities. A popular local MP, he was nevertheless infamous for never making a single speech in his twenty eight years in the Commons, though he did instruct Prime Minister Clement Attlee to "Change the bloody record" as he threw a coin at him — an incident which had him briefly debarred from the Commons.
Legge-Bourke died in 1973 whilst still a Member of Parliament. The by-election to replace him was won by Liberal Clement Freud.
Legge-Bourke inherited a fraction of the Lord Great Chamberlainship of England, succeeded by his son, William. His daughter-in-law (The Hon. Mrs Legge-Bourke, Lord Lieutenant of Powys) was made a lady-in-waiting to Queen Elizabeth II. His granddaughter, Alexandra Legge-Bourke, known as "Tiggy," was nanny to Princes William and Harry. Another granddaughter, Eleanor Legge-Bourke, is a television personality in France.