Short answers, pulled from the story.
The United Kingdom of Great Britain and Ireland officially formed on the first of January 1801. This new sovereign state emerged from the merger of Great Britain and Ireland under the Acts of Union.
Napoleon was defeated at the Battle of Waterloo in 1815 by the armies of the Duke of Wellington and Gebhard Leberecht von Blücher. Britain financed the coalition that defeated France and held together the Congress of Vienna in 1814-1815.
Over one million deaths were caused by the Great Famine when potato blight hit Ireland in 1846. Another million emigrated within a few short years, with most migrants going to Britain or the United States.
The Reform Act 1832 added 217,000 voters to an electorate of 435,000 in England and Wales. This act broke the logjam in parliamentary representation for the first time as growing industrial cities gained seats.
Germany gave up agreeing to an Armistice on the 11th of November 1918 after massive spring offensives failed. By early 1916, the government imposed conscription to keep army strength up since volunteer numbers were falling off.
The state was renamed the United Kingdom of Great Britain and Northern Ireland on the 12th of April 1927 with the Royal and Parliamentary Titles Act. Six northeastern counties opted out of joining the Free State and remained part of the Union since being governed under limited home rule since 1920.