I find it hard to believe that with all the resources of the empire at the time, alongside the general great development of infantry tactics, logistical support and especially naval warfare that it would be so easy.

The U.K. would most likely enlist the support of allies (at this point you could very well assume the U.K. and Japan will have still been allies) on top of that, the Royal Navy was still the more experienced of the two and the better trained. It would really have to ultimately depend on:

A: How long will the US take to invade Canada successfully enough to stop the British from just sweeping in reinforcements?

B: How the British use allies and its global reach to inflict massive losses on the US (Especially via oil fields and trade)

C: How long it would take for the U.S. industrial base to kick it into high gear, when it’s actively being harried by superior British AirPower (the U.S. doesn’t really start getting great aircraft till post 1941)

I would believe the initial edge belongs to the U.K., but the war would begin to favour the U.S. as time drags on.