If you genuinely think we smell, you should visit France, eww.
^ Stereotypes, while usually incorrect, are not entirely un-substantiated. They must begin somewhere as truth, even if eventually blown out of all proportion. Probably the biggest stereotype of the British is the whole teeth thing, which for most people is completely untrue, but the culture here is vastly different to America. The culture is not as much aesthetically focused in this country as it is over there, so things like theeth are probably immediately obvious to an American who is used to watching American television where everyone has perfect (chemically whitened/fake) teeth. The point is, stereotypes on such a large scale MUST be somewhere along the line based in truth.
It's simple, over here we are genrally more concerned with what we would consider more important things than finely honing our perfect self image. Whereas in America, to a lot higher percentage of people, image is vastly more important than most things. While there are people here who are concerned with nothing but image and there are people in the states not at all concerned with image, the mindset of the general populous in the one is more focused on self image and the other more focused on stuff like education