Quite frankly, if a Brit told me it was definition of a bad pizza, I would merely tell them they don't know pizza!
I know it probably sounds a bit snobby of me, but when it comes to things that *I* think are fairly distinctly American, I don't expect too many Brits to know beans about what makes for good (insert fairly distinctly American food item).
Probably the only place I've seen anything deep dishy thus far is Pizza Hut. I know, I know...but so far it's the best I've seen. Although we DO have a Chicago Rock Cafe about a 10 minute walk from us that we haven't tried yet, so I'm hopeful there may be some decent pizza about!