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Reginald Gervase Alexander was the son of Dr. William Alexander of Blackwall Lodge, Halifax, West Yorkshire, Yorkshire (3 September 1806 – 13 April 1888), Fellow of the Royal College of Physicians of London and Justice of the Peace for the West Riding of Yorkshire, and wife (married 4 October 1837) Emily Kirby (died 26 April 1862), daughter of Samuel Kirby of Grove House, Sheffield, West Riding of Yorkshire, Yorkshire. He had an older brother, Arthur William Alexander (2 August 1843 – 15 February 1895), who died unmarried and without issue. His uncle Gervase Alexander (30 September 1802 - 23 September 1871) married his aunt Eliza Kirby on 16 October 1838, while his aunt Ellen Alexander (10 December 1803 – 27 September 1854) married John Clarke Prescott (died 16 May 1863) on 20 February 1839.
In February 1857, he was admitted to Heath Grammar School, Halifax. In 1867, he was admitted to St John's College, Cambridge. He graduated from University of Cambridge, Cambridge, Cambridgeshire, with a Master of Arts degree and from University of Edinburgh, Edinburgh, Midlothian, with a Doctor of Medicine degree, and became a Fellow of the Linnean Society of London.
The Committee for Privileges and Conduct of the House of Lords declared on 22 July 1912 that he was one of the co-heirs of the titles of Baron Burgh and Baron Cobham (of (Cobham, in) Kent) (except for the attainder), and on 11 May 1914 that he was one of the co-heirs of the title of Baron Strabolgi. He never had, however, the chance of succeeding in any of these titles, nominately to the Barony Cobham, since the attainder that had fallen on Henry Brooke, 11th Baron Cobham in 1603, though finally removed in September 1916, was only lifted after his own death.
Marriage and issue
- Gervase Disney Alexander, 15th Baron Cobham (of Kent) (6 May 1880 – 10 June 1933)
- Hon. Mary Isabel Alexander (born 11 June 1882), who married twice, firstly on 27 April 1916 to John Leslie Morton Shaw (died 18 December 1925), son of John Edward Shaw, and secondly on 21 May 1927 John Bazley-White (died while on active service during World War II circa November 1940), son of John Bazley-White, without any issue from both marriages, and was granted the rank of a baron's daughter on 9 May 1917
- Robert Disney Leith Alexander, 16th Baron Cobham (of Kent) (23 April 1885 – 21 February 1951)
- Hon. Muriel Helen Alexander (born 15 March 1887), married on 4 March 1916 to John Edmund Burnett Thornely, son of Thomas Thornely, from Cambridge, Cambridgeshire, and was granted the rank of a baron's daughter on 9 May 1917, whose two sons Gervase Michael Cobham Thornely (born ca. 1918), married on 5 April 1954 to Jennifer Margary Scott, daughter of Sir Hilary Scott, with four children, two sons and two daughters, and John Alexander Cobham Thornely (ca. 1921 - 31 January 1966), unmarried and without issue, became the heirs in abeyance of their maternal uncle the 16th Baron.