In 1714 he matriculated to New College, Oxford, and became a student of the Middle Temple the following year. Verney sat in Parliament as a Tory, speaking out against the Whig Prime Minister Robert Walpole. In 1726 he switched sides, however, and Walpole made him a judge in Wales as a reward.
In 1727 he became a King"s Counsel, and in 1728 a Bencher at Lincoln"s Inn, having switched Inns some time earlier.
In the 1727 election he campaigned in Radnor, but lost and was again returned for Downton. In May 1729 he was made Attorney General to the Queen Consort, Queen Caroline.
He resigned from his Welsh post in 1732 due to ill-health, but in 1732 accepted an appointment as Chief Justice of Cheshire. After the death of Sir Joseph Jekyll on 19 August 1738, Verney applied to succeed him as Master of the Rolls, and was accepted after the position was turned down by Sir John Strange.
He took office on 9 October 1738, and was sworn in on 12 October.
After a few years, his ill-health made it impossible to continue as Master of the Rolls, and he offered his resignation to the Lord Chancellor in early 1741. In May 1741 he was again elected for Downton, but he died on 5 August.
He was called to the Bar in 1721, and in an attempt to gain contacts for his work as a barrister he became a Member of Parliament (Member of Parliament) for Downton with the help of his brother-in-law, Anthony Duncombe, in 1722.