He served as a Research Associate at Brown University, in Providence, Rhode Island. In 1971 appointed lecturer in the Department of Chemical Engineering and Chemical Technology at Imperial College, London. He was successively Reader in 1979, Professor of Chemical Physics in 1985, and head of the Department of Chemical Engineering in 1988.
In 1996 he was appointed Pro-Rector (Research) and subsequently also Deputy Rector and Pro-Rector (Resources) at Imperial College, holding these positions simultaneously, and overseeing the college's medical school formation in 1997 from the merger of St Mary's Hospital Medical School, Charing Cross and Westminster Medical School (formerly Charing Cross Hospital Medical School and Westminster Hospital Medical School), the Royal Postgraduate Medical School and the National Heart and Lung Institute.
In 2007 the then Secretary of State for Innovation, Universities and Skills, Rt. Hon. John Denham MP invited him to chair a review of UK physics which reported in October 2008.
He is a Visiting Professor at Imperial College. He is a member of the Engineering and Physical Sciences Research Council (EPSRC) and chairs their Resource Audit Committee. He is a member of the South East England Development Agency (SEEDA) Board. He is a member of the European Union expert panel on philanthropy and universities. He is UK Chair of the British-Italian Partnership Programme.
He was knighted in the 2009 Birthday Honours. He was President of the Institution of Chemical Engineers 2011–2. He is a Chartered Engineer, Chartered Physicist and Fellow of: the Royal Academy of Engineering; the Institution of Chemical Engineers, the Institution of Electrical Engineers, the Institute of Physics and Imperial College London He ia a Touloukian Medal holder from the American Society of Mechanical Engineers (1997) and holds honorary degrees from Lisbon University, Exeter University, Loughborough University
He married first in 1969, Christina Marjorie Stone and they had one son. They divoced in 1974. He married second Sylvia Frances Tolley in 1978 and they had two sons.
- List of University of Southampton people
- University of Southampton page announcing Prof Wakeham's knighthood and summarising his career
- "List of Fellows".<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
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- The London Gazette: . 13 June 2009.
- www.icheme.org News 23 May 2011 "Sir William appointed new IChemE president"
- 2003 Fellows of Imperial College Announced
- Exeter Honorary Degree
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- Wakeham, Sir William (Arnot)’, Who's Who 2014, A & C Black, an imprint of Bloomsbury Publishing plc, 2014; online edn, Oxford University Press, Dec 2013; accessed 2014_01_26