Have a fascist rising begin in England around the same time as they did in Germany and Italy, Have FDR get his way on more of his reforms and make a socialist USA, have the Axis win World War II with British support.
Allow a communist/socialist leadership in the USA by 1930; never let it join NATO in '49. America would ally with the USSR and Communist Cuba and proceed to convince some socialist Latin American countries to join the ComIntern.
The UK simply does not have the industrial capacity, military power, or national wealth/resources to actually have any kind of sustained, long-term ideological conflict with the US. Maybe if the US goes Commie (but in that case, Britain and all of Europe probably do too).
A bigger BNA and a smaller US results from a different ARW and over time the future Canada gets even bigger while the US annexes Mexico and Central America after several conflicts. Canada is given Kingdom status and the "UK" evolves into an international union of Britain and many OTL Dominions.
While in Europe Napoleon never returns to power in France and Prussia annexes Saxony and is backed by Russia. France and Britain are against this but they do not want to renew fighting and a sort of cold war between Britain and France vs. Prussia and Russia with Austria sifting allegiance takes place. The US and the future Germany go to war and the US wins while the unresolved conflict with Britain and France erupts into a world war which the German-Russian alliance loses, Russia dropped out of the due to a radical ideology inspired revolution and the Tsars are overthrown but the revolutionary state that replaces it is very weak. The US doesn't have a revolution but is taken over by a radical party and establishes friendly relations with the new Russian government.
After the world war, Canada (apart of the UK) and the US are left as the worlds remaining powers while China reforms and becomes a third force in the world but generally keeps to itself and East Asia. The Second Cold War between the US and the UK (mainly Canada) is about to begin.
The POD doesn't have to be before 1900 just when it happens by UK I mean Great Britian and I don't care about How long it goes for and It has to Be the UK leading one side and the US leading the other, not The UK backing Germany or US backing USSR or anything like that