All noted politicians or Prime Ministers.
Mr. Sheridan may refer to either the playwright, Richard Brinsley Sheridan (1751-1816), who was known as a great orator and who entered parliament in 1780, or to his grandson, Richard Brinsley Sheridan (c.1806-1888), who entered parliament in 1845.
Mr. Burke refers to Edmund Burke (1729-1797), who was a prominent author, political theorist, orator, and statesman.
Lord Castlereagh refers to Robert Stewart (1769-1822) who, as a British statesman, held many offices including Chief Secretary for Ireland, Secretary of State for War and the Colonies, and Foreign Secretary. He finally served as Leader of the House of Commons until his suicide.
Viscount Sidmouth refers to Henry Addington (1757-1844), who served as Prime Minister from 1801 to 1804. He was called upon to become Prime Minister following the resignation of his childhood friend William Pitt, the Younger, who had left the office due to a dispute with King George III (1738-1820).
Mr. Canning probably refers to George Canning (1770-1827), who served as Foreign Secretary and Chancellor of the Exchequer before briefly serving as Prime Minster. He remains the shortest serving Prime Minister of Great Britain. His son, Charles John Canning, 1st Earl Canning, briefly served in the House of Commons before his succession to a peerage caused him to move to the House of Lords.