Walpole resigned as Prime Minister in February 1742. Barnard was subsequently a supporter of the proposal for an enquiry to investigate Walpole's actions over the preceding ten years with a view to making charges of corruption. He was one of the 21 members named to the enquiry, but little progress was made as most of those called as witnesses refused to testify. The only substantive allegation – that of bribing electors in the districts of Wendover and Orford – failed when it became clear the evidence was essentially hearsay. Barnard supported a subsequent motion to introduce a Bill of Indemnity pardoning witnesses from any crimes if they testified against Walpole or his Ministers, but the legislation was defeated in the House of Lords.
