Monkhouse, a Cumberland man, was Surgeon on HMS Niger from 1763 on the Newfoundland station. In 1766 the 32-gun frigate was joined by Joseph Banks and his schoolfriend Phipps as supernumeraries intending to use the Niger's routine fisheries protection duty off Newfoundland for a botanical and zoological collecting field trip. Bank's friendship with Monkhouse began when he went down with malaria when the ship was anchored at Croque. The two came together again in 1768 when Monkhouse was appointed Surgeon on the Endeavour on Cook's first voyage of 1768-71. Cook noted early on that Monkhouse's 'care and vigilance' had helped to keep down scurvy. In addition to such routine duties, Monkhouse played a full role on the voyaage, joining Banks on his forays ashore in South America and at Tahiti, taking supplementary readings of the Transit of Venus on Moorea and, again with Banks, exploring the interior. Monkhouse died of malaria in November 1770 at Batavia on the voyage home and was succeeded as surgeon by his mate, William Perry.

Park of Monkhouse's Endeavour Journal (6-21 Oct. 1769) is in the British Museum ('Cook's Second Voyage. Fragments', Add, ms 27889)