Skeet was born in Auckland, New Zealand and was educated at King's College, Auckland and the University of Auckland. He served with the New Zealand Army and Navy during World War II. He was a barrister and solicitor at the Supreme Court of New Zealand and was called to the English Bar in 1947 by Inner Temple. He was a member of the Council of the Royal Empire Society.
Skeet first stood for Parliament in Stoke Newington and Hackney North in 1951 and Llanelli in 1955. He was elected Member of Parliament for Willesden East in 1959, losing the seat in 1964. He was then MP for Bedford 1970-83 and North Bedfordshire 1983–97. Ahead of the 1992 election, he survived a deselection attempt by his constituency party. In the 1992-1997 Parliament, Skeet rebelled frequently against John Major's ailing government, on issues such as the Maastricht Treaty; Skeet was a staunch Eurosceptic. Indeed, Skeet was one of only eight Conservative MPs who voted against Major's government more than 50 times.
- https://www.academia.edu/10809077/Rebels_and_rebellions_Conservative_MPs_in_the_1992_Parliament,p.88. Retrieved 26 March 2019; https://www.telegraph.co.uk/news/obituaries/1469555/Sir-Trevor-Skeet.html. Retrieved 26 March 2019
- https://www.academia.edu/10809077/Rebels_and_rebellions_Conservative_MPs_in_the_1992_Parliament,p.88. Retrieved 26 March 2019.