There IS NO DOUBLE TAX. Simply, you pay local taxes. IF the taxes you pay are less than US income tax, then you pay Uncle Sam the difference.
I am friends with someone who works in the UK. It is way, WAY more complicated than what you state. It's true that there isn't an outright double tax, but she definitely pays more than just the higher of the two. There are many accidental "gotchas" because for the most part, the tax code of the two countries is written with no thought given to special circumstances such as living abroad.