He contested the parliamentary seat of Paddington North for the Conservative Party in the 1955 general election, but was unable to unseat the Labour incumbent, Ben Parkin.

He was shortlisted in 1957 as a prospective candidate for Warwick and Leamington, the seat vacated by the retirement of Prime Minister Anthony Eden, but Sir John Hobson was selected ahead of him.

Goodhew was an early member (1962) of the Conservative Monday Club, formed to combat the influence of the Bow Group on the Government's African policies.

He took part, with four other MPs, in a Club public meeting in January 1962 which affirmed support for Sir Roy Welensky and the Central African Federation, and Rhodesia, and criticised the policies of the then Colonial Secretary, Iain Macleod.

He suffered a heart attack in October 1973 and had coronary bypass surgery; he resigned his post as a whip on medical advice.

However, he went on to serve as a Member of the Speaker's Panel of Chairmen from 1975 to 1983, and on the Select committee for House of Commons Services from 1978 to 1983.

He steered a Private Member's Bill to the statute book, to allow "death-bed" marriages to take place outside licensed premises.