Brodie was born at Winterslow, Wiltshire, on 20 August 1778, being the eldest son of the Rev.
He early chose law as a profession, but in consequence of an asthmatic complaint, he devoted himself to conveyancing, and became a pupil of Charles Butler.
One of the drafts by which he was earliest known was that of the Rock Life Assurance Company, 1806, a model for similar instruments, and only departed from where some variation was rendered necessary, as in the charter of King's College, London, which he also drew in 1829.
Soon after the presentation of the first report it was determined to bring in bills founded upon its recommendations, and Brodie prepared that for abolishing fines and recoveries, which was brought in at the end of the session 1830, and became law in 1838.
He was the author of a A Treatise on a Tax on Successions to Real as well as Personal Property, and the Removal of the House-tax, as Substitutes for the Income-tax, and on Burdens on Land and Restrictions on Commerce and Loans of Money, 1850.