Sous-secrétaire d'État parlementaire
Mitchell served in the Thatcher Ministry as Parliamentary Under-Secretary of State for Industry, 1979–1981, Parliamentary Under-Secretary of State at the Northern Ireland Office, 1981–1983, and then Parliamentary Under-Secretary of State, 9 June 1983 – 9 January 1986, and Minister of State, 9 January 1986 – 25 July 1988, at the Department of Transport. He was knighted in 1988 upon his resignation from Government.