 At the 1964 general election, he was elected as Member of Parliament (MP) for Gravesend in Kent, a marginal seat which was normally won by the party forming the government.Indeed, Murray held the seat until it was regained by the Conservatives in 1970, the year Edward Heath became Prime Minister.From 1969 to 1970, he was a junior minister in Harold Wilson's government, as Parliamentary Secretary to the Ministry of Transport, under Minister of Transport Richard Marsh.