Well, I've learnt a lot of British English. I also gave up on the idea of going to school in the UK because it's really competitive there, although I thought it was interesting to learn about A-levels, GCSE, Sixth form, and FE Colleges.
I haven't really got as good a sense of the culture as I would have hoped, though. All I'm really seeing here are people and political ideas that mirror those of more urban and liberal parts of the US. With all the arguments about White Privilege, distrust of Islam, and attempts to balance globalisation with protectionism, everything seemed familiar. I mean, the Protestants want their values respected and talk about being the foundation of the country's moral principles, the people complain about the high rent in the big city and long commutes, there's a lot of talk about wealth inequality, etc.
The society seems like what I imagine many New England states or California might look like if they were independent of the rest of the US and unburdened by things like the Second Amendment. Incredibly high prices, more public transit, a national healthcare system, no guns, and less of the national budget being spent on defence.
Of course, my impressions are only based on this forum and what I read from various news networks. I haven't actually been there to see how it is. So, ultimately, my impression of the UK is that it's a society similar to many parts of US, and that the differences that do exist lie on the extremities of the culture in habits and quirks rather than at the core. The rhythms of life, the arguments, the types of people you think about, and the attitudes tend to be pretty similar. Although maybe that's just because the people here are so young... maybe older people in the UK would show more difference? I'm not sure.