Until he succeeded to the estate, Welby was a partner in the Newark banking house of Welby & Co.
Listed a Treasury supporter after his re-election, Welby opposed Catholic relief throughout in 1813. After entering on his inheritance, he became a doubtful attender. He took leave of absence on 25 Mar. 1816, but was present to vote against Catholic claims on 21 May. He was in the majorities on Admiralty salaries, 17 Feb., and for the suspension of habeas corpus, 23 June 1817. His never voting against ministers and his inactivity were criticized on the hustings in 1818, but he headed the poll.
