Ha, so you admit it. You didn't in fact answer the part of the question about uniforms. As I said: "only sexy_jag has answered the part of the question about uniforms". My point was that you seemed to be ignoring the high level of similarity in UK police uniforms because it didn't fit in with your hypothesis that all UK police forces were different. You only answered half the original question.
Surely a badge isn't a uniform. The first online definition I came across was "n. an identifying outfit or style of dress worn by the members of a given profession, organization, or rank". And outfit (to me) means clothes. Therefore any badge would be excluded from the definition of uniform. I mean, if you included badges, then you could say the army doesn't wear a uniform.
I only included the London shirts because I forsaw that some pedantic people would say " but in London they can wear different coloured shirts". So I was just heading off that comment. Actually, I believe (not sure) that the shirt colour is an option rather than a compulsion.
And I mentioned the word 'police' because that seems to be the only thing US police cars have in common. They seem to have all white, pale blue, dark blue, the famous black & white and probably others. I wasn't using the existence of the word on the car as an exception.
Do correct me if I'm wrong, but I believe all UK standard police patrol cars are (in underlying body colour) white. They all have the same colour chequerboard (or they are supposed to, anyway). There are differences in other logos. But not to the extent that (myself, anyway) have ever seen one and thought "is that a police car?"