In 1963, Meyer was selected to fight the constituency of Eton and Slough, then held by Labour's leftwing internationalist Fenner Brockway. In the 1964 General Election, Meyer won the seat by 11 votes, gaining respect by ignoring his constituency party's advice to campaign on the race issue, which could have swung a number of votes in that constituency at the time. His was one of only four Conservative gains in that election. Recognising that he would only be in the seat temporarily, Meyer made the most of his time in Parliament, advocating Britain's joining the Common Market and strengthening the United Nations. He also established himself on the liberal wing of the party: voting to abolish capital punishment and for sanctions against Rhodesia. In the 1966 General Election he lost his seat to Labour's Joan Lestor by 4,663 votes.