He is a nephew of the former Independent Labour Party leader and World War I conscientious objector, James Maxton.

He was educated at Lord Williams's Grammar School, Thame, and subsequently attended University College, Oxford.

He was selected to oppose the sitting MP, the Shadow Secretary of State for Scotland, Teddy Taylor, at the 1979 general election in the Glasgow Cathcart constituency.

In 1983, his constituency was redrawn to his disadvantage, but Maxton ruled out a move to any neighbouring and more favourable areas; he therefore notionally gained his seat from the Conservatives again in the 1983 general election.

He stood down from the House of Commons at the 2001 general election and was given a life peerage on 17 June 2004, as Baron Maxton, of Blackwaterfoot in Ayrshire and Arran.