My theory on why white Americans look different from their British counterparts is that Americans tend to have more mixed ancestry. For example, a study that I read a while ago estimated that approximately 80-85% of African-Americans had significant white ancestry while 30-40% of white Americans had significant African-American ancestry.
The one-drop-rule has kept European Americans pure while diluting AAs actually. The reason why American Whites look different than Brits is because their gene pool is from all over Europe and it is recent in comparison.