He joined the Territorial Army with a commission in the Northumberland Fusiliers in 1934.

Murton was Member of Parliament for Poole from 1964 to 1979, preceding John Ward.

Murton was a government whip under Edward Heath and later a Deputy Speaker of the House of Commons from 1973 to 1979.

He was appointed as a Privy Counsellor in 1976, and after his retirement from the House of Commons at the 1979 general election, he was given a life peerage as Baron Murton of Lindisfarne, of Hexham in the County of Northumberland on 25 July 1979.

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