I don't notice a huge difference between the supermarkets, to be honest. I mean, I occasionally find navigating the aisles of the supermarkets here to be a bit of a sh*tshow, but I think that's because they are more narrow than they are at the t-rex of a Stop & Shop I would use back home, and I always end up shopping at peak times because that's when I can go.
I shop at all the locals (Co-op, Sainsbury, M&S, Waitrose) and the cashier service has been pretty standard to me. I usually have my own bags, which they appreciate, so I toss my own stuff in them pretty quickly, but I've never felt rushed while doing it. Having been on the other side (cashier for all the high school/college jobs), I always make eye contact, end all phone calls before I'm at the till, and take out my earphones if I've had them in. So people are usually pretty friendly and courteous, and I am as well.
I think the only place I've had bad customer service here is HSBC (phone wise. my local branch is great)