Brown was born in Slinfold, Sussex. He studied mathematics and philosophy at Christ Church, Oxford. He took medical training at King's College London and graduated MBBCh in Oxford in 1914. He worked as a neurologist in France and returned to his post at King's College London where he earned a DM in 1918, MRCP in 1921 and was elected FRCP in 1930.
In 1936 he became the director of the Institute of Experimental Psychology at Oxford University. He was a Christian and had a life long interest in parapsychology. He served on the board of the Society for Psychical Research 1923-1940.
in 1952 he became President of the British Psychological Society
- Mind and Personality: An Essay in Psychology and Philosophy (1970)
- Personality and Religion (1946)
- Psychological Methods of Healing; An Introduction to Psychotherapy (1938)
- Mind, Medicine and Metaphysics: The Philosophy of a Physician (1936)
- Science and Personality (1929)
- Suggestion and Mental Analysis: An Outline of the Theory and Practice of Mind Cure (1922)
- Burt, C. (1952). Dr. William Brown Obituary. British Journal of Psychology: Statistical Section, 5, 137–138.
- Sutherland, J.D. (1953). William Brown, D.M., D.Sc., F.R.C.P. Obituary. British Journal of Medical Psychology, 26, 1.