McQuarrie was born in Greenock. He was educated at Greenock High School and the Royal College of Science and Technology, Glasgow. He became a design consultant and served as a councillor on Greenock Town Council 1949-55.
McQuarrie unsuccessfully contested Kilmarnock in 1966, and Caithness and Sutherland in October 1974. He was Member of Parliament (MP) for East Aberdeenshire from 1979 to 1983, gaining the seat from the Scottish National Party's Douglas Henderson with a majority of only 558. He was then MP for Banff and Buchan from 1983 to 1987, when he lost his seat to future SNP leader Alex Salmond. In the House of Commons he was Chairman of the British Gibraltar All Party Group. Following the death of Denis Healey on 3 October 2015, McQuarrie became the second-oldest surviving former MP, after Ronald Atkins.
McQuarrie was knighted in 1987.
- Greenock Telegraph
- The Times Guide to the House of Commons, Times Newspapers Ltd, 1966 & 1987
- Leigh Rayment's Historical List of MPs [self-published source][better source needed]
- A Lifetime of Memories, December 2013, published by The Memoir Club
- Hansard 1803–2005: contributions in Parliament by Albert McQuarrie
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