The United Kingdom was formed in 1800 with the Act of Union between the Kingdoms of Great Britain and Ireland; Great Britain itself being formed in 1707 with a similar act of Union between the Kingdom of Scotland and the Kingdom of England (incorporating Wales) in 1707.
The UK also controlled many overseas territories, a legacy of a former empire developed both after its formation, and by its constituent countries beforehand. Due to the divergence, the status of the empire and the Commonwealth of Nations is a mystery.
Dialogue suggests that the country was ruled by a queen before the outbreak of the Great War..
No details are known about the state of the British Isles after the Great War. However, in the 23rd century, Allistair Tenpenny left the country for the Capital Wasteland in the United States to seek wealth and fortune, hinting at some of the possible conditions in post-War Britain. The ancestors of Colin Moriarty also left Ireland for the Capital Wasteland shortly after the Great War for unknown reasons.
"Allistair Tenpenny came to the Capital Wasteland from Great Britain to seek his fortune, so that alone tells you that the U.K. was also hit in the war. And if he came to U.S. to succeed, that says a lot about how screwed up Europe must be. So we just allude, a little bit, to the state of the rest of the world. We like to leave a lot to the players' imaginations, and somebody like Tenpenny serves as a catalyst for those thoughts." - Emil Pagliarulo