Same for British English more or less, though
Coffee Bar would be more likely than
Coffee Shop (which to me sounds Japanese) I think, and those would be a lot posher than a
cafe - especially without an accent (ie
cafe rather than
café). In Britain a
cafe (pronounced
caff or
caffy) is often very downmarket and serves traditional English food. It's where for example lorry drivers might stop and get their eggs and bacon for breakfast (is this what you call a
roadhouse in AmEng???) Often in fact called a
transport cafe. Not to be confused with a café with the accent (pronounced
caffay) which might be posher.
However, last time I was in the UK people didn't seem to be using any of the terms any more. They just said they were going to Starbucks