In 1704 he was promoted to chief justice of Brecknock on the South Wales circuit through Harley's influence.
At the 1705 general election Coxe was involved in a double return at Cirencester with Henry Ireton.
He petitioned but then withdrew on 15 November, leaving Ireton to be declared duly elected.
It was claimed that he did so to avoid a scrutiny by the House of the bribery that been practised by both sides, which would have damaged his position as a judge.
At the 1713 Bathurst asked Coxe to make way for one of his brothers at Cirenccester, while the other seat was taken by Thomas Master.
[1] With the change of regime in 1714 Coxe was dismissed from his post as judge, but was returned again as MP for Gloucester at the 1715 general election.