With a P.O.D. around the American Civil War (it can be earlier but the war must occur and it must result in a Union victory) can you strain U.K.-U.S. relations to the point where the two countries find themselves on opposing sides of a "Great War" analogue?
Hard mode: no "Britain and France support the Confederacy"
Britain refuses to pay a penny to the United States regarding the Alabama claims (perhaps Disraeli is PM at the time instead of Gladstone?), irritating the US, which in retaliation provides some clandestine backing for the latter Fenian Raids, which are more serious than IOTL. Although the Fenian Raids get beaten back and die out, there is more bad blood between the US and the UK in TTL mid-1870s.
Queue forty years of the US and UK occasionally stepping on each other's toes around the world, say in China or Hawaii or Venezuelan borders or Mexican oil fields. None of the incidents themselves are very serious, but they serve to keep the US at least still anti-British. When TTL WW1 rolls around, the US is pro-German neutral instead of pro-Entente neutral. While staying out of the conflict for a while, the US eventually gets irritated over the British distant blockade in much the same way the Americans were angered by German USW IOTL, and declares war on the UK.