I was in London in late May/early June. The major difference I noticed between London and US attire was the lack of two items : jeans and shorts. With one exception, the only jeans I saw were on construction/maintenance workers on break, and shorts were almost as rare. I brought along two "skorts" (look like knee-length skirts, but have pant legs inside) and was glad I had them, as there was a heat wave (in the 80's) while we were there. My husband, of course, didn't have the skort option, but he doesn't mind the heat as much as I do and was comfortable in long pants.
As for the question of why one would not want to look obviously American : I think that the statement someone made about contempt and avarice was misleading. When my husband and I opened our mouths, our nationality became obvious, but we never experienced any rudeness as a result. One very good reason not to advertise your tourist status while in Europe is that petty criminals, mostly pickpockets, recognize tourists as easy prey, since they tend to carry cash and electronics and will not be around long enough to file charges against those who steel from them (fortunately, I get this information from reading and not from personal experience). A less dire reason is that standards of casual dress *are* somewhat higher (though not extremely so) in London than most places in the US, and, just as you might treat a person in ripped and dirty clothing a little differently than someone with a neat appearance, a Londoner could conceivably form a negative first impression of a person whose casual dress went over the line into sloppiness according to local standards.