He was educated at Edinburgh High School and Jesus College, Cambridge,[1] and was called to the Bar, Lincoln's Inn, in 1823.
Brougham was appointed a Master in Chancery in 1831, which he remained until the following year.
In 1868 he succeeded his elder brother as second Baron Brougham and Vaux according to a special remainder in the letters patent, and was able to take a seat in the House of Lords.
Lord Brougham and Vaux married Emily Frances, daughter of Sir Charles William Taylor, 1st Baronet, in 1834.
Lord Brougham and Vaux survived her by two years and died in January, 1886, aged 90, at Brougham Hall, a gothic revival mansion, the building of which was largely overseen by William before he succeeded Henry as Baron Brougham.