Marshall was educated at Humberstone Foundation School (also known as Clee Grammar School for Boys for Boys and became the comprehensive Matthew Humberstone School in September 1973) on Clee Road in Old Clee, Cleethorpes, and Magdalen College, Oxford, where he took double first class honours in mathematics and was awarded a University Junior Mathematical Prize in 1961. He gained a PhD from the University of Liverpool in 1965. He became a mathematics university lecturer and a Methodist local preacher. He served as Vice-president of the Methodist Conference in 1992.
In a 1971 by-election, Marshall was elected as the Member of Parliament (MP) for Goole. From 1976-9, he served as Parliamentary Private Secretary to the Home Secretary, and as Chair of the Select Committee on Trade and Industry. He left Parliament in 1983, when the Goole constituency was abolished in boundary changes.
In 1985 Marshall transferred to the Social Democratic Party and subsequently became a member of the Liberal Democrats. He fought Bridlington for the SDP in 1987, coming second. He rejoined the Labour Party in 2015. In 2015 he became a Trustee of the Parliamentary Outreach Trust.
Marshall is the author of two published books: Parliament and the Public (Macmillan 1982) and Business and Society (Routledge 1993).
In 1969 he married Margaret Pamela Antill in Enfield. They have a daughter (born 1975).
- Times Guide to the House of Commons, 1966 & 1979
- Leigh Rayment's Historical List of MPs [self-published source][better source needed]
- Yorkshire and the Humber Liberals Democrats website
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