In 1796, the ill health of his eldest brother, Miles Barne, who was already quite reluctant to be a member, left the family seat of Dunwich vacant (Dunwich was a notorious "
Rotten Borough" and remained in the pocket of the Barne family from 1764 until the
Great Reform Act). Given that the elder brother,
Barne Barne, had been appointed Commissioner of Taxes in 1791, it fell upon Snowdon Barne, who had not been "making that progress in his profession which … might have been expected", to take over the seat. during that time, he voted in favour of the Government, making clear his desire for a place on the Custom Board. His support in several Bills during 1811 and 1812 saw this realised and he was appointed to that Board in 1812. ==Later life and death==