There is no plausible way this could ever happen. But in the world of implausibility, here's a TL.
1925 - FDR dies of long terminal complications of polio.
1929 - Great Depression has worse effect on US.
1932 - Electoral politics crazy. Republicans run Hoover, Democrats split into populist far right and far left movements. Rightists win election, US slides quickly into a populist form of fascism with social welfare, nativist/racist policies, and military build up as another way of putting people to work. During national emergency, election of 1936 is postponed, US becomes authoritarian but not a true fascist dictatorship - retains trappings of being democracy (think Putin's Russia), aggressive and imperialist in Latin America, but isolationist in Europe and Asia.
1939 - WW2 breaks out as in OTL. USA is strictly neutral, no aid or government favoritism. US is not favoably disposed to German Nazis because they are seen as "too" extreme and a potential risk down the line.
1940-41 - German campaigns victorious as in OTL. Without US lendlease and tactit US assistance, War in Atlantic goes worse for Britain. BoB also goes worse and British start to run out of raw materials for industries quicker. Churchill Government, in desperation, approaches US with offer of a transtlantic Anglo-American federation to preserve Britain from complete collapse. US Congress, dominated by National Democrats, force thru a number of Constutional Amendments and in late 1941 enough States ratify.
By Treaty of Halifax, signed on the Deck of HMS Prince of Wales, the Anlgo-American Commonwealth is established with the following provisions:
(1) The USA, Britain, and the British Empire establish a confederation in which Great Britain is allowed to retain its monarchy and internal governmental structure, but all British colonies and Dominions must revoke relationships to Britain through the crown; the US President becomes Head of State for the entire Commonwealth, except for Britain, which is permitted to retain King George VI as head of state until his death, at which time the Britain must undertake a plebecite every 4 years regarding abolition of the monarchy; the CoE must be disestablished. All Canadians, Australians, New Zealanders and Britons become US citizens, all US citizens become also British citizens. The status of the "non-white" inhabitants of other British colonies is let for later to determine. In the interim, they are treated as joint US/British mandates.
1941 (there is no Japanese attack on the US in this TL because the US reached accomodation with Japan in the Chinese Partition of November 21, 1941)
1943 War breaks out between Germany and the US. Britain becomes major staging area of bombing campaign and eventuaul invasion of Europe. US troops and civilians stationed in Britain with joint US/British citizenship. US wins war in 1946 after atomic weapons introduced. Many US service people and others stay in Britain, and others move in.
1946-1988 Britian becomes thoroughly Americanized with large American-born voting population. In plebicite of 1979, monarchy is abolished and the US president becomes the formal Head of State for all citizens of the Anglo0American Confederation (which by now has divested itself of most former British colonies)
1988 American emmigration, coupled with declining native-British birth rate gives US-born residents voting majorities in Parliament.
1990 Act of Parlimentary Dissolution formally eliminates the residual British governmental structure, Great Britain is broken up into 4 States (Ulster, Wales, Scotland, and England) with US-style bicameral legislatures and admitted to the United States. Shortly thereafter British Columbia ("now Pacific Columbia"), Manitoba, Saskatchewan, Yukon, and Ontario join US as States. Quebec, Labrador, and Newfoundland become independent commonwealths. Australia and New Zealand become completely independent republics.