We use “soft power” and economic/trade warfare. No one can match our military but we actually rather always use economic leverage first and only force when absolutely necessary or personal(public is pissed like seen after 911 and Iraq. Bull seeing red or in modern era green/Islam/half moon).It's not the worth of the islands, it's the principle of resisting armed aggression against an ally. What if China invaded American Samoa? It's not worth much, and it's very far away, but the U.S. would fight to take it back.
The UK is very economically dependent on US. We use cultural warfare like Soviets did too. We would not resist openly just mock, criticize(not politicians but media so “free press”) and raise trade barriers gradually so masses notice less