Nedham belonged to a family long established in Jamaica, but neither he nor his father lived there. In 1774, six weeks before the dissolution, he was returned at Winchelsea on the Nesbitt interest. At the general election he contested Wallingford in company with T. F. Wenman, and supported by Lord Abingdon, but was forced to decline soon after the poll commenced.1London Chron. 8-11 Oct. 1774. He was returned for Winchelsea in January 1775 in place of Arnold Nesbitt, who chose to serve for Cricklade. Nedham voted consistently against North’s Administration. In 1780 he was returned for Pontefract by his friend Robert Monckton Arundell, Lord Galway, whose wife was a distant relative. He voted against Shelburne’s peace preliminaries, 18 Feb. 1783, and in March was classed by Robinson as a follower of Fox. Though he did not vote on Fox’s East India bill, 27 Nov. 1783, he is invariably referred to as a supporter of the Coalition. At the general election of 1784 he was once again returned for Winchelsea on the Nesbitt interest. No vote by him is recorded during this Parliament, but he paired against Pitt over the Regency, 1788-9. He appears never to have spoken in the House.
He died 27 Apr. 1806, aged 65.