In World War II, Oakley served with the Royal Signals as a subaltern. He then studied science at Exeter College, Oxford. Later he became a Fellow of the Institute of Physics and the British Computer Society. In 1950 he joined the Telecommunications Research Establishment (TRE) where he undertook research in telecommunications and civilian applications of military research. He then worked in Whitehall as a civil servant, joining the Ministry of Technology under the Harold Wilson government in 1969. Subsequently, he became the chief official of the Science and Engineering Research Council (SERC).
Oakley was director of the United Kingdom Alvey Programme (1983–87), a British government-sponsored research programme for projects in the area of information technology, initiated as a reaction to the Japanese Fifth generation computer project. He went on to be chairman of the software company Logica. He chaired the managing board of the Computer Centre of the University of London, an important UK supercomputing centre, and was a director of the European Initiative for Quantum Computing.
From 1988–89, Oakley was president of the British Computer Society. In 1991, on hearing that British Telecom planned to dispose of its site at Bletchley Park for housing, together with Tony Sale, he helped to save the site and establish the Bletchley Park Trust and became a director of the Trust. He was chairman of the Computer Conservation Society from 1996 to 2000.
- "Death announcement: Brian Oakley". The Daily Telegraph. 21 August 2012. Retrieved 21 August 2012.
- Campbell-Kelly, Martin (Winter 2012). "Obituary: Brian Wynne Oakley". Resurrection: The Bulletin of the Computer Conservation Society. 60: 34.
- Honorary Graduates — Brian Wynne Oakley, CBE, University of Essex, UK, 9 July 1998.
- Brian Oakley and Kenneth Owen, Alvey: Britain's Strategic Computing Initiative, MIT Press, 1990. ISBN 0-262-15038-7.
- Martin Campbell-Kelly, Review of Alvey: Britain's Strategic Computing Initiative, Business History Review, Vol. 64, No. 3, pages 570–572, Autumn, 1990. JSTOR.
- BCS Past Presidents Archived 3 October 2007 at the Wayback Machine, British Computer Society, UK.
- Clarke, Gavin (29 August 2012). "RIP Brian Wynne Oakley: Saviour of Bletchley Park". The Register. UK. Retrieved 28 December 2012.
- Honorary Awards Archived 8 June 2009 at the Wayback Machine, Sheffield Hallam University, UK.