Burton then studied law, entering the Inner Temple in November 1819, and was called to the bar in November 1824. He was recorder of Daventry in 1826–1827, and a puisne judge of the supreme court at the Cape of Good Hope 1828–1832, and then transferred to the Supreme Court at Sydney. In July 1834 he went to Norfolk Island to preside over the trial of some convict leaders who had mutinied. Thirteen were sentenced to death, but as no clergy were on the island, Burton reprieved them until their cases could go before the executive council and clergy could be sent to the island. He endeavoured also with some success to improve the miserable conditions of the convicts; Burton being a religious man, arranged that two of the prisoners should act as catechists to the others until clergy could be procured. Eventually both Protestant and Roman Catholic chaplains were appointed. Burton gave an account of the position at Norfolk Island in his book "The State of Religion and Education in New South Wales", (1840). Two years later he published "The Insolvent Law of New South Wales, with Practical Directions and Forms".