He was a protégé of John Taylor, who began his education, and, on becoming divinity tutor at Warrington Academy, placed Palmer (1756) at school in Congleton, Cheshire, under Edward Harwood.
In 1764 he became minister of King Edward Street Chapel, Macclesfield, and also kept a school there.
There was an orthodox secession from his ministry; he consequently resigned in 1779, and moved to Birmingham without regular charge, being in independent circumstances.
At Birmingham he renewed his acquaintance with Priestley, and was a member of a fortnightly clerical club which arranged the material for the Theological Repository.
In 1782 Priestley recommended him, but without effect, as colleague to Joseph Bretland at Exeter.