His brother Edmund, a solicitor who practised in Daventry, had several children, including Sir William Westbrooke Burton (1794–1888), a judge and statesman in Australia, whose second wife was Charles' granddaughter Maria Alphonsine West.
[2] He was befriended by the leading Irish barrister John Philpot Curran, who persuaded him that his future lay in Ireland.
He made his reputation with his speech for the defendant, which was described as "a masterpiece of eloquence", in the leading quo warranto case, R. v. Waller O'Grady, in 1816, where the Crown challenged the right of Standish O'Grady, 1st Viscount Guillamore, the Chief Baron of the Irish Exchequer to appoint his younger son as a Court clerk.
[3] His most memorable trial was that of Daniel O'Connell for conspiracy in 1844: while there were several judges on the Court, it was Burton who passed the sentence of imprisonment, which was later quashed by the House of Lords.
[4] However one obituary of the judge maintained that O'Connell, in general, a stern critic of the Irish judiciary, actually admired Burton.