He attended Thetford Grammar School from 1855 to 1860 and then a private academy from 1860 to 1862, where he discovered an interest in natural science.
[4] Palmer became a teacher in Cambridgeshire for a short time, but in 1863 started work for a chemist in Bury St. Edmunds.
He also worked for the Brymbo Steelworks Company where he was appointed chief chemist, but had to leave after two years due to ill health.
Palmer's first work on local history was The Town, Fields and Folk of Wrexham in the Time of James the First (1883), based on a 1620 survey of the Lordship of Bromfield and Yale by John Norden.
It was originally unveiled by Lord Howard de Walden at the old Wrexham Public Library on Queen's Square on 29 November 1922.