He was educated at the University of Paris and then at the University of London. He won a law scholarship in 1849 and was called to the bar at Lincoln’s Inn in 1850. In the following years he built a substantial legal practice, which he maintained throughout his parliamentary career. He acted as counsel in various celebrated trials, such as the Tichborne case (1869).
Matthews entered the House of Commons in 1868, having won the borough of Dungarven for the Conservatives. Indeed, he lost his seat to a supporter of Irish Home Rule in 1874 and failed to win it back in 1880. In the 1885 and 1886 general elections, he was elected M.P. for East Birmingham. Also in the latter year, as a result of his personal friendship with Lord Randolph Churchill, he was appointed home secretary, thus becoming the first Catholic cabinet minister since the passing of the Catholic Emancipation Bill in the late 1820s. This meant that the ecclesiastical patronage of his office, which involved dealing with the offices and tides of the Church of England, was handled by the First Lord of the Treasury. However, he proved a poor home secretary, being likened to a “French dancing master” by one critic.
In the opposition from 1892 to 1895, Matthews did not participate in the debate surrounding Gladstone’s introduction of a bill to remove the remaining legal sanctions against Catholics (popularly known as the Russell and Ripon Relief Bill), and he voted against a bill calling for the disestablishment of the Welsh Church. His Conservative politics had obviously tempered his religious convictions. On the return of the Salisbury government in 1895, he was raised to the peerage as Viscount Llandaff. He continued to play a part in politics, though a diminishing one, until his death on 3 April 1913.