For this to be plausible, the USA would had to have been more antagonistic. Let's assume they invade Mexico and create a puppet state to reduce the risk of anyone being able to open a home front against them by convincing Mexico. As many of you know, Germany tried to feel this out during WWI, but ultimately the US found out and Mexico had declined anyway.
If that happens, perhaps the UK could believe their Caribbean and Central American colonies would be at risk. However, I do not know how we make that the greater risk than a Germany that could conquer Europe. If France has a successful fascist coup, maybe that would help.
At best, maybe we could alter the scenario a bit? How about a Fascist France, Germany, Japan, Italy (and maybe Spain) against the United States. The UK stays neutral because it is threatened by both sides (in this scenario, I still believe the UK would actually join with the Americans). Those four powers could probably force the United States to retreat to the continental mainland, but it is unlikely that the "Super Axis" would be able to successfully invade the nation. I bet they could trounce on the USSR, though. That many troops would just be too much, and without the UK holding them up in the Middle East (again, we are assuming UK neutrality), and Africa.
Creating a scenario where the UK teams up with anyone besides the US, or even stays neutral, seems extraordinarily unlikely, however. I don't think it is really even in the realm of possibilities if we are just accounting for something after WWI. US-UK relations had been rapidly improving since the UK turned down supporting the rebellious Confederate States of America in the American CIvil War during the 1860s.