The Corn Laws were enacted in the early 1800s to limit imports of foreign grain and protect the profits of British farmers. Highly unpopular with ordinary people because they increased the price of bread, the laws were seen to favour the interests of the land-owning classes. They were repealed in 1846 during the Prime Ministership of Sir Robert Peel (1788-1850).
The 'Duke' was the Duke of Wellington (1769-1852), Prime Minister of Britain from 1828 to 1830, and a prominent politician in the House of Lords until his retirement.
Lord Palmerston (1784-1865) was initially Secretary of War, then Foreign Secretary, and eventually Prime Minister from 1855 to 1858, and from 1859 to 1865.