Musgrave was born at Washfield in Devon, and was educated at the University of Oxford. There he was elected to a Radcliffe travelling fellowship, and he spent several years abroad. In 1766 he settled at Exeter, but moved to Plymouth to improve his career prospects.
Everything went wrong when he published a pamphlet in the form of an address to the people of Devon, accusing certain members of the British government of having been bribed by the French government to conclude the Treaty of Paris (1763), and declaring that Chevalier Charles d'Eon de Beaumont, the French minister plenipotentiary to England, had in his possession documents which would prove the truth of his assertion.
Eon de Beaumont denied all knowledge of any such transaction and of Musgrave himself, and the House of Commons in 1770 decided that the charge was unsubstantiated. The discredited Musgrave was obliged to earn a meagre living in London by writing until his death, in reduced circumstances. He wrote several medical works, now forgotten; and his edition of Euripides (1778) was a considerable advance on that of Joshua Barnes.
- See William Munk, Roll of the Royal College of Physicians, ii (1878)