As the scion of a famous business family in North East England, Palmer took an interest in shipping and the large industrial works on the Tyneside. By the time of his death, he had become Chairman of Marley Hill Chemical Company and managing director of John Bowes and Partners, colliery owners, in both of which concerns his half-brother, Sir Alfred Molyneux Palmer, who had inherited the Palmer baronetcy; was a director. Godfrey was also chairman of Chislet Colliery Ltd and had other business interests in London. He travelled widely on business trips, visiting the Far East, India, Australasia, and the Americas. Palmer also served in the Territorial Force. He achieved the rank of Major in the Yorkshire Regiment.
Politics
It was no surprise that Palmer followed his father into Liberal politics as he had followed him into business and industry. Sir Charles Palmer had been MP for North Durham from 1874 until 1885 when the seat was abolished. He then transferred to the constituency of Jarrow which he held from 1885 until his death in 1907. Sir Charles Palmer's death caused a by-election in Jarrow and the local Liberal Association adopted Mr Spencer Leigh Hughes, a London-based journalist and later MP for Stockport as their candidate. In that contest the Liberal vote was split by the candidacy of an Irish Nationalist and Hughes lost the election to Labour. Jarrow Liberals therefore had cause to look for another candidate and in 1909, Godfrey Palmer was unanimously invited to be the Liberal candidate at the next election. Palmer was regarded as a strong candidate for the Liberals in Jarrow, given the family name and local connections and was expected in some quarters to win the seat back from Labour while other commentators felt the Unionists had a better chance of beating Labour there. In the event this conflict of opinion was reflected in the result which revealed Jarrow as a very close three-way marginal. Palmer gained the seat from the sitting Labour MP, Pete Curran, by the narrow majority of 67 votes, with the Conservative Mr J Kirkley just 217 votes behind the winner. At the second general election of the year in December 1910, Palmer held his seat, again in a three-way fight, this time with a majority of 111 but on this occasion it was Kirkley for the Unionists who crept into second place ahead of a new Labour candidate. By the time of the 1918 general election, Palmer had aligned himself with the Lloyd George Coalition Liberals. He was not opposed by the Conservatives and presumably received the Coalition coupon. In a straight fight against Labour's John Hill, Palmer got 61% of the poll and a majority of 4,510 votes. He chose not to contest the 1922 general election and did not stand for Parliament again.