Col. Burton, twin brother of Henry, 1st Marquess of Conyngham, sat for county Clare in the last two Irish parliaments, though also elected for the family borough of Killybegs. The borough was disfranchised at the Union, the compensation being £15,000. Burton supported government at Dublin and Westminster and expected attention in return. In July 1801 he was allowed to nominate the sheriff of Clare, but soon afterwards threatened to desert government with his brother because a Union promise to make a family friend in county Clare a baronet had not been fulfilled. The lord lieutenant pacified Conyngham.
Burton, who was a candidate for office as early as 1793, was disappointed in 1804 when he asked for the government of Bermuda. He agreed to wait for another opening.
Nothing was done for Burton. Listed a supporter at the election of 1806, he went over quietly to the Portland ministry in 1807. The Home secretary suggested that Burton be offered a place at the Irish treasury board if Vereker refused it, so as to link his family with the ministry. On 22 July 1807 Burton was informed that he would be appointed lieutenant-governor of Lower Canada in the spring, an arrangement that ‘ought to be kept secret, otherwise your successor in the county of Clare would meet with great difficulties’. There was a delay in the appointment and Burton, who had attended ‘every night’, without speaking as usual, did not vacate until July 1808. About the end of October Burton was still not appointed and Castlereagh wrote to Spencer Perceval:
I am sure the Duke of Portland will feel that after the repeated assurances given to Col. Burton that all was arranged, and after he has sacrificed his parliamentary situation upon the faith of such assurance, that the office should not be withheld from him till surveys are made, and a township in Canada divided.
NLI, Richmond mss 70/1322; Wellington Supp. Despatches, v. 124, 480; Wellington mss, Wellesley to Manners, 17 Mar., to Perceval, 10 June 1808; Perceval (Holland) mss 22, f. 66.
So Burton was appointed to a sinecure which did not require his residence in Canada, though he went there, returning in September 1812 with the idea of re-entering Parliament. The chief secretary wrote, 3 Oct. 1812, ‘Mr Burton has determined, I understand, after some doubt in regard to his lt. governorship, to stand’. To resolve the doubts, Burton was prepared to resign the office if he could name his successor, or yield it up if he thereby strengthened his brother’s claims for a marquessate. On 14 Oct. Lord Bathurst reported, ‘He will be better pleased to keep his place and not come into Parliament’.