He was educated privately by Mr. Graham, father of Sir Robert Graham, one of the barons of the Court of Exchequer. At the age of eighteen years he traveled to Geneva and, after a short residence there, made a grand tour of the continent.
In 1745 Barrington put forward a plan for a new national militia whose units were to be based on the parish. In the autumn of that year, he visited Dublin to take his seat as an Irish peer. He was appointed a lord commissioner of the admiralty on 22 February 1746, and on 14 December was appointed to a committee being formed “to manage the impeachment” of Simon, Lord Lovat, for high treason—a proceeding that ended in Lovat s conviction and execution. Barrington subsequently wrote a paper justifying the conduct of the admiralty board. His paper on quarantine in 1751 also received considerable attention.
In 1754 he was appointed Master of the Great Wardrobe and in the same year was elected to Parliament as member for Plymouth. He was sworn a member of the Privy Council on 11 March 1755 and was again elected to represent Plymouth after his acceptance of the office of secretary at war on 21 November 1755. This post involved the preparation of army expense estimates for Parliament, as well as the issue of orders for troop movements, although major troop movements were always arranged by the secretaries of state.
On 21 March 1761 Barrington was appointed chancellor of the exchequer, succeeding Mr. H. B. Legge. Barrington held this office until he replaced George Grenville as treasurer of the navy. He continued in that position until he resumed office as secretary at war, on 19 July 1765, at the king’s express wish. Barrington remained in this office until 16 December 1778, when in recognition of his long public service he was awarded a pension of £2,000. The Civil List was relieved briefly of the expense of this pension in January 1782, when Barrington was appointed joint postmaster general; but the pension was renewed at the king’s insistence when Barrington was removed from office the following April. Barrington died on 1 February 1793 and is commemorated by a memorial in the chancel of Shrivenham Church, Berkshire.
After his return to England (on 21 February 1738), he was elected as M.P for Berwick-upon-Tweed in March 1740, just in time to oppose the administration of Sir Robert Walpole, whose political power terminated with the first session of the new Parliament in 1741. Barrington represented Berwick until 1754, and Plymouth from 1754 to 1778.