Born George Winn, he was the only son of Pelham Winn, of South Ferriby, Lincolnshire, by Elizabeth Wighton, daughter of Reverend Gilbert Wighton by Elizabeth Allanson, sister of William Allanson, of Bramham Biggin, Bramham, Yorkshire.
[1][3] He was elected through his connection with William Lawrence, who managed the elections in Ripon, brother-in-law of the widow of Allanson-Winn's cousin Charles Allanson (who had previously represented Ripon in Parliament).
He continued to represent Ripon until 1798,[1][3] during which time he was a silent supporter of William Pitt the Younger's administration.
[1] He was rewarded four years later when he was made an Irish peer as Lord Headley, Baron Allanson and Winn, of Aghadoe in the County of Kerry.
He died in April 1798 and was succeeded in his titles by his eldest son, Charles.