6 March] 1748[2] in Dover Street, Piccadilly, London, the eldest son of William Coxe (c. 1710 – 1760), a physician to the king's household, and his wife, Martha, daughter of Paul D'Aranda.

[1] He was the older brother of the writer and poet Peter Coxe (c. 1753–1844),[1] who wrote the poem "Social Day".

He wrote prodigious and detailed accounts of his travels with Lord Herbert around the Swiss and French Alps, which were subsequently published.

In 1803, Coxe married Eleanora, daughter of William Shairp, consul-general for Russia, and widow of Thomas Yeldham of St Petersburg.

[3] Coxe's literary style featured a detached, unemotional, objective voice that, though typical of the historiography of his day, came to be seen as arch[5] and quaint[6] by later generations.