Downton Abby is getting all the publicity, but if anyone likes the sort of thing, just 'cause it's British, I'd recommend Rosemary and Thyme. I like this show, did years ago when it ran on my then local PBS, but now I have re-discovered it.
I'll warn you now, I also liked Red Dwarf, so I won't claim to be very high brow, but R&T is an excellent modern drama. Neflix has a lot of things going for it, I have to say. Detective Linley, Father Brown, etc. I'll leave to each of you to find something you enjoy. I just got a free subscription, thanks to a good friend, but I'll update here on other things I find.