You can't really just lump "all British people" into one category. No matter where you go in the world there will be different types of people- nice, mean, rude, friendly, etc. Not all British people will have the same opinion of americans. 
I agree with this post. It all boils down to who you meet. I'm here doing a course in the politics department so I hear things about America from both ends of the spectrum

When I first arrived I expected to see anti-Americanism but when you do see it, it's generally not what you expect. At least, that's how it was for me. However, I imagined that I would see some pro-Americanism and when I saw it, it wasn't what I expected.
The British students I have met in my course have a good opinion about the set-up of American judicial system, 'lots of powerful rhetoric,' as one student said once to me. A lot of them have said to me that we Americans are lucky to not have to fit the bill for a royal family.
I suppose I have seen a lot of 'grass is greener on the other side' syndrome. For example, because I'm from Texas so more than one person I have met over here has assumed that I'm 100% for the death penalty. I'm actually 100% anti-death penalty and all the Texans I met/know are also either completely against it or are sensitively on the fence about the issue. I was actually surprised when I spoke to a few British students about it and the census among them was that they fully supported it.
I'm in London so I wouldn't say I get a
lot of attention for being American. Again, I'm from Texas so that is packed with a bunch of stereotypes already, if you know what I mean

Every once in a while someone will hear my accent, whether it be in the markets or on the street when I'm with friends and they'll ask the universal question, 'where are you from?' I imagine it was a bit of a novelty for my friends, having an American friend, but it wore off. Now they don't really bring up the fact that I'm American.
A lot of the people I have met here think the strange aversion to universal health-care in the US is ridiculous and don't understand why so many are against it. I just reply that the 'American health system is the devil, but it's the devil they know.' It gets mentioned a lot, but probably do to the focus now with Obama and reform.
I guess to conclude I will say that a lot of the people I have met in the UK, both British and EU, have a good opinion about Americans. Better than I expected tbh

Again, you can't lump all of British people into a nice little category. But I bet you'll meet people who are against American institutions or simply can't wait to tell you all about the fun they had on a trip they had to America. Expect to see opinions on all sides, but when you see it, I'm sure you'll be surprised.