Reginald Palgrave was born in Westminster, London, the fourth son of Francis Palgrave and his wife Elizabeth Turner, daughter of banker Dawson Turner. His brothers were Francis Turner Palgrave, William Gifford Palgrave, and Inglis Palgrave. He became a solicitor in 1851; but two years later was appointed a clerk in the House of Commons, becoming clerk of the House on the retirement of Sir Erskine May in 1886. He married Grace Battley, daughter of Richard Battley, in 1857. He was made a Companion of the Order of the Bath (C.B.) in the 1887 Golden Jubilee Honours and advanced to Knight Commander of the Order of Bath (K.C.B.) in 1892, and retired from his office in January 1900. He died in Salisbury in 1904.
- The Chairman's Handbook; The House of Commons: Illustrations of its History and Practice (London, 1869)
- Cromwell: an appreciation based on contemporary evidence (London, 1890)
- Palgrave also helped to edit the tenth edition of Erskine May's Treatise on the Law, Privileges, Proceedings and Usage of Parliament (London, 1893).
- Biography and Genealogy Master Index. Farmington Hills, Mich.: Gale, Cengage Learning. 1980- 2009.
- Lee, Sidney, ed. (1912). . Dictionary of National Biography (2nd supplement). 3. London: Smith, Elder & Co.
- "Wilts Obituary". The Wiltshire Archaeological and Natural History Magazine. Wiltshire Archaeological and Natural History Society: 415. 1904. Retrieved 21 May 2019.
- "No. 25712". The London Gazette. 5 January 1888. p. 3361.
- "No. 26319". The London Gazette. 23 August 1892. p. 4817.