Peacock was the son of Lewis Peacock, a solicitor. After practising as a special pleader, he was called to the bar in 1836 by the Inner Temple, and joined the Home Circuit. In 1844 he obtained great reputation by pointing out the flaw which invalidated the conviction of Daniel O'Connell and his fellow defendants. He took silk in 1850, and was elected a bencher of the Inner Temple the same year.
In 1852, Peacock went to India as a legal member of the Governor General's Council. The Legislative Council was established soon after his arrival, and although no orator, he was so frequent a speaker that legislation enjoining councillors to deliver their speeches sitting was said to have been devised with the sole object of restraining him. As a member of Lord Dalhousie's council he supported the annexation of Oudh, and he stood by Lord Canning all through the Indian Mutiny.
In 1859 Peacock became the last Chief Justice of the Supreme Court of Judicature at Fort William, and was knighted. He was appointed as the first Chief Justice of the Calcutta High Court on 1 July 1862. He returned to England in 1870 and in 1872 was appointed as a paid member of the Judicial Committee of the Privy Council, the court of last resort for the British Empire.
- This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). "Peacock, Sir Barnes". Encyclopædia Britannica. 21 (11th ed.). Cambridge University Press. p. 20.