With John Courtney MP, in 1798 Burdett supported the campaign of Catherine Despard to publicise and protest the conditions under which her Irish husband Colonel Edward Despard and other political radicals were held in Coldbath Fields Prison following the suspension of habeas corpus. Together they were instrumental in securing a parliamentary inquiry, and as a result Burdett was for a time prevented by the government from visiting any prison in the kingdom. Edward Despard, a member of the London Corresponding Society and a United Irishman remained in prison for three years. In 1803, after Despard was tried and (notwithstanding Horatio Nelson's intervention as a character witness) executed for treason, Burdett helped secure Catherine Despard a pension.