I can't speak for other Americans but THIS American won't lose 1 seconds sleep worrying about what Briton's think.
The crux of the matter. The sun never sets on the American Empire these days.
"The forces of the United States military are located in nearly 130 countries around the world performing a variety of duties from combat operations, to peacekeeping, to training with foreign militaries. Some of these deployments have existed for nearly 50 years, as in Japan, Germany, and South Korea, while other deployments have more recent origins such as the current occupation of Iraq.
As of January 2005, there are some 250,000 soldiers, sailors, airmen, Marines, and Coast Guardsmen deployed in support of combat, peacekeeping, and deterrence operations. This figure does not include those forces normally present in Germany, Italy, the United Kingdom or Japan unless bases at those locations are actively supporting a combat operation. Furthermore, tours of duty in these locations are routine and not considered hardship tours. If one were to include these forces the number of deployed troops worldwide would be around 350,000."
Ditto, but oh, how defensive we can get!