West was the son of Dr. West, Prebendary of Winchester, who married the sister of Sir Richard Temple, afterwards Lord Cobham. He was originally designed for the church, but entered into his uncle's regiment of horse, which after some time he quitted for a post in the office of the secretary of State, where his promotion was impeded by his uncle's opposition to the Ministry. He quitted this situation in disgust for another of uncertain and remote advantage, that of clerk extraordinary of the Privy Council, which was obtained for him in the year 1729; but it was not till 1752 that he succeeded to the regular clerkship. It is to West's credit that during these disappointments he never forgot the cultivation of his morals and talents, and that even the drudgery and dulness of an office, did not extinguish his love of literature. With West, that school of poetry originated, which has produced Akenside, Gray, Mason, and the Wartons.