When Violet chastises Edith for having submitted an article to a newspaper, Edith defends herself by mentioning Lady Sarah Wilson, who was Britain's first woman war correspondent in WW1.
Robert says the religious leader coming for dinner is 'toffee nosed'. This means he's a snob and stuck up. The phrase dates to the mid 19th century when rich men at Oxford were called 'toffs', because they wore special gold tufts on their caps on certain occasions.
Violet remarks, "Lady Gregory, Countess Markievicz... why are the Irish rebels so well born?" This is in reference to Countess Constance Markievicz, a member of Sinn Fein who was born Constance Gore-Booth, a daughter of a baronet and who later married a Polish count; and the Irish nationalist Augusta, Lady Gregory, who was born into an aristocratic Anglo-Irish family.
The fictional burning of the (also fictional) Lord Drumgoole's Irish manor house that Branson is implicated in is based on actual events. The destruction of country houses in Ireland was a phenomenon of the Irish revolutionary period (1919-1923), which saw at least 275 country houses deliberately burned down, blown up, or otherwise destroyed by the Irish Republican Army. The vast majority of the houses, known in Ireland as Big Houses, belonged to the Anglo-Irish aristocracy and were symbolic of the 18th and 19th-century dominance of the Protestant Anglo-Irish class in Ireland at the expense of the native Roman Catholic population.
The "Mr. Shortt" Cora refers to is Edward Shortt, who was the Home Secretary in Prime Minister David Lloyd George's cabinet from 1919 to 1922.