Alexander was a member of
Reading County Borough Council from 1972 to 1974 and of
Berkshire County Council from 1973 to 1977. He was on the Board of the Housing Corporation 1977–1980, of the Economic and Social Research Council 2003–2009, and of the Accounts Commission for Scotland, 2002–2008. From 2008 to 2009, he served as chair as Postwatch Scotland. From 1999 to 2002 he was Chairman of
West of Scotland Water Authority and from 2002 to 2006 he was Chair of
Scottish Water, a post from which he resigned after a major disagreement with Scottish Ministers about the content of the delivery plan for the company's capital programme. In 1991, Alexander conducted an independent inquiry into the large losses incurred by Western Isles Council (
Comhairle nan Eilean Siar) as a result of the collapse of the Bank of Credit and Commerce International. In 2009 he chaired a review, sponsored jointly by
Research Councils UK and
Universities UK, of the operation of Full Economic Costing of Research in UK universities. He was elected a Fellow of the Academy of Social Science in 2015. In October 2018 Alexander was appointed to the Board of Audit Scotland as an independent non-executive member. He was Chair of the Audit Scotland Board, 2020-2024. Alexander was appointed an Officer of the
Order of the British Empire (OBE) in the New Year Honours List, 2010. ==Publications==