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, and at its peak led the largest empire in human history. Due to the divergence, the status of the empire, the Commonwealth of Nations, and the overseas territories is a mystery.
The relationship between the United Kingdom and the Irish state are unknown, since Ireland did not officially declare itself a republic or leave the Commonwealth of Nations until 1949, which is after the divergence of 1945. The capital city of Wales is also unknown; while it is Cardiff in our world, Cardiff did not become the Welsh capital until 1955.
The United Kingdom was a member of the European Commonwealth until it's dissolution in 2060. The UK bickered with other former members of the Commonwealth over the last remaining drops of oil on Earth, sparking a bloody conflict known as the European Civil War.
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.
In Fallout Tactics, Sharon's family is claimed to stretch back to the English county of Essex. In addition, one of Martin's ancestors once ran a software company in England that ended up going out of business.
"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