The son of John Palmer, wig-maker, he was born at Norwich.
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. He entered Warrington Academy in 1759. Joseph Priestley was, from 1761, one of his tutors.
In his last year he was constant supply (14 May 1763 to 15 August 1764) at Allostock, Cheshire.
He then kept a school at Macclesfield, Cheshire. In 1772 he became minister of King Edward Street Chapel, Macclesfield.
There was an orthodox secession from his ministry. He consequently resigned in 1779, and moved to Birmingham without regular charge, being in independent circumstances.
Palmer died of paralysis at Birmingham on Tuesday, 26 December 1786, and was buried in the Old Meeting graveyard on 2 January 1787.
Priestley preached (8 January) his funeral sermon.
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.