He was born on 23 September 1743, in Southampton Street, Bloomsbury, London where his father, John Combe, carried on business as an apothecary.
On 5 April 1784, he was admitted by the Royal College of Physicians a licentiate in midwifery; on 30 June, he was nominated a governor of St. Bartholomew's Hospital.
He had also a substantial private practice, and made a collection in materia medica, which was purchased by the College of Physicians shortly after his death.
Combe was appointed one of the three trustees to whom Hunter (who died in 1783) left the use of his museum for thirty years, after which the collection passed to the Glasgow University.
Combe also published a work on ‘large brass’ coins, entitled Index nummorum omnium imperatorum, Augustorum et Cæsarum ..., London, 1773.
Horatii Flacci Opera cum variis lectionibus, notis variorum et indice completissimo,’ 2 vols.
[1] He wrote the memoirs prefixed to the sale catalogue of Richard Southgate's library, and contributed to the appendix to George Vertue's Medals of Thomas Simon, 2nd edit.