Peacock was admitted to the Inner Temple in 1828, and practised for several years as a special pleader until he was called to the bar in 1836, joining the Home Circuit.

His speciality, owing to his training and physique, was in arguing refined points rather than imposing his will upon common juries.

Peacock, despite his junior standing, pointed out a flaw that, although technical, could not be refuted by those representing the case against O'Connell.

Following this success, from which Peacock’s subsequent fame and distinction is thought to have arisen, he practised on the back benches until he took silk on 28 February 1850.

In 1859, Sir James Colvile stood down as Chief Justice of the Supreme Court of Judicature at Fort William.

Peacock succeeded him in this role and was simultaneously made Vice-President of the Legislative Council of India, as well as receiving a knighthood.

In 1862, the Indian judicial institutions were remodelled and Peacock’s position was replaced by the Chief Justice of the High Court at Calcutta, a role he assumed on 1 July.

Amongst other cases he would deliver judgement on Hodge v The Queen, La Banque d'Hochelaga and another v. Murray and others, Peacock passed away from heart failure on 3 December 1890, at the age of 85 in his home at 40 Cornwall Gardens in South Kensington.