Brown was the son of F. J. Brown and was born at Basingstoke and educated at Luton Grammar School, Queens' College Cambridge and Cuddesdon Theological College, Oxford. In 1935 he married Florence Blanche Marshall.
Brown was secretary of the Southwark Diocesan Reorganisation Committee from 1946 to 1960 and secretary of the South London Church Fund from 1952 to 1960. He was also chairman of the Church of England Youth Council from 1961 to 1966.
- The Times, 23 January 1970, "Church News: Two New Bishops Appointed"
- Newbigin, Lesslie (2009) Unfinished Agenda: An Updated Autobiography (Wipf and Stock) p. 230
- McLean, D. (12 February 1994). "Obituary: The Right Rev Laurence Brown". The Independent. Retrieved 9 February 2020.
- Who Was Who 1897–2007. London, A & C Black, 2007 ISBN 978-0-19-954087-7
- The Times, 1 September 1960, "Ecclesiastical News: New Bishop Suffragan of Warrington"
- The Birmingham Post Year Book and Who's Who 1973-74