I've gotten pintos at the Weston Tesco, Morrisons, and Sainsburys. Haven't found black beans at any of them, though.
I also had a very frustrating time finding something like great northern beans. The best I found were haricot beans, which were a little smaller than I wanted.
I've been meaning to get Tesco's dry bag called 'Exotic bean mix'. It looks like it might be a mixture of the types of beans I used in one of my soups back home.