I think it's easier to explain than you think (and, for once, not at all due to the class system at all).
Britain has been under relentless cultural assault from the US for decades. It is no secret, and no surprise, that it was Friends that introduced "can I get a" to the UK. This trend has accelerated with the Internet, where all English speakers tend to move towards the ubiquitous American English.
Even something like programming acts as a vehicle for this. Try colouring something grey, for example.
Language is a very tangible, day-to-day way of asserting cultural independence. See how France used to sing Eurovision in French every year. Sadly, even they now sing songs in English.
This taps into a deep-seated concern in some of the British population that it will become a cultural 51st state. Certainly we identify more with the US than any of continental Europe. This is not necessarily unwarranted, but I think it unlikely. Even something as uniquely American as hip-hop was taken, adopted by young disadvantaged Londoners and transformed into grime instead. Britain's identity is formed by more than the media it consumes and it creates, but by the people who inhabit it.
FWIW, I really do hate "could care less" as it's literally the opposite of what meaning is trying to be conveyed. I've personally picked up "bathroom" over "toilet". I think it's a great euphemism, which is, in itself, a traditionally British thing to do.