Brougham was the second son of Henry Brougham and his wife Eleanor. She was the daughter of James Syme and the niece of William Robertson. His older brother was Henry Brougham, 1st Baron Brougham and Vaux, who served as Lord Chancellor, and one of his younger brothers was William Brougham, 2nd Baron Brougham and Vaux, who sat also in the Parliament of the United Kingdom as well as succeeded in the barony.
Brougham entered the British House of Commons in 1826, having been elected for Tregony. He represented the constituency until 1830 and sat then for Downton in the following year. In 1831, he was returned for Winchelsea. After a year the constituency was abolished and Brougham stood successfully for Kendal, which had been established by the Reform Act 1832. In the same year his brother Henry made him Registrar of Affidavits as well as Clerk of Letters Patent. Both offices were provided with a high salary and were executed by deputies. Brougham died already in the next year on Brougham Hall, unmarried and childless, aged 53. His burial took place in Skelton, Cumbria and was only attended by his brothers.
- Urban (1834), p. 331
- Ferguson (2009), p. 340
- Cokayne (1912), p. 342
- Stenton and Lees (1976), p. 50
- Urban (1834), p. 332
- Ferguson, Richard Saul (2009). Cumberland and Westmorland MP's from the Restoration to the Reform Bill of 1867, 1660–1867. BiblioBazaar Llc. ISBN 1-113-67443-1.
- Sylvanus, Urban (1834). The Gentleman's Magazine. part I. London: William Pickering.
- Michael Stenton and Stephen Lees, eds. (1976). Who's Who of British Members of Parliament: 1832–1875. Brighton: Harvester Press. ISBN 0-85527-219-8.
- Cokayne, George Edward (1912). Vicary Gibbs, ed. The Complete Peerage of England, Scotland, Ireland, Great Britain and the United Kingdom. vol. II. London: The St Catherine Press Ltd.
- Hansard 1803–2005: contributions in Parliament by James Brougham
|Parliament of the United Kingdom|
|Member of Parliament for Tregony
With: Stephen Lushington
James Adam Gordon
|Member of Parliament for Downton
With: Charles Shaw-Lefevre 1830–1831
Thomas Creevey 1831
Philip Pleydell Bouverie
|Member of Parliament for Winchelsea
With: John Williams
|New constituency||Member of Parliament for Kendal