He was educated at Rugby School and Magdalen College, Oxford, where he matriculated on 27 July 1826, and was elected to a demyship.
In 1833 he proceeded MA and gained the chancellor's prize with a Latin Oratio de Comœdia Atticorum which was printed the same year.
With extreme high church views, Palmer anticipated in an unpublished Latin introduction to the Thirty-nine Articles, composed for the use of his pupils in 1839–40, the argument of the celebrated Tract XC.
A difficulty was the recent admission to communion by the English chaplain at Geneva of Princess Galitzin and her eldest daughter, both of whom had renounced the Greek church.
His claim for admission to communion in the Russian church, pressed for nearly a year, was at length rejected by Filaret, Metropolitan of Moscow.
On his return to England in the autumn of 1841, Palmer submitted to Bishop Charles James Blomfield, as ordinary of continental chaplains, the question which Archbishop Howley had ducked, and received an affirmative answer.
The œcumenical character of the Greek church Palmer admitted; he also renounced and anathematised the forty-four heresies, but demurred to their alleged presence in the Thirty-nine Articles.
On the question whether what he had done amounted to a renunciation of the churches of England and Scotland, he appealed to Bishop Luscombe and the Scottish Episcopal College.
Soon after the decision of the privy council in the Gorham case in 1852 Palmer again sought admission to the Greek church, but recoiled before the unconditional rebaptism to which he was required to submit.
The chief thing I fought him on was his attempt to defend the absurd assertion of some Romish manual that the Times is the organ of the Anglican Church.
He tried to make out that it fairly represented the dominant spirit of the Church.’ For the rest of his life Palmer resided at Rome in the Piazza di Santa Maria in Campitelli, where he died on 4 April 1879, in his sixty-eighth year.
During his stay in St. Petersburg Palmer edited R. W. Blackmore's translation of Andrei Nikolaevich Muraviev's History of the Church in Russia, Oxford, 1842.
He issued, however, its notes and appendices as Aids to Reflection on the seemingly Double Character of the Established Church, Oxford, 1841, and treated the same topic in an anonymous work.