He qualified as a solicitor in 1819, when he began to practise at 11 Staples Inn, Holborn in London. In 1820 he moved to 11 King"s Bench Walk, Temple, and in 1822 to 27 King Street, Cheapside. In 1831 Burn was appointed registrar of marriages at chapels prior to 1754.
In 1836 he became secretary to the commission for inquiring into non-parochial registers, a post which he retained until 1841.
Burn died at The Grove at the age of 71. Burn married firstly Sarah Sophia Colnett at Street Lawrence Jewry on 17 April 1822.
They had a daughter Ellen, but Sarah died.