Hi there,
The fashion police aren't waiting at the door in London or anyplace else in Europe (although there is the Monte Carlo casino). I've seen everything from spike heels in the Louvre to combat boots at the theater, so no worries- wear what's comfortable for you. I do think that you might suffer from some foot fatigue or injury, though, because Crocs aren't the most supportive shoes and could get a little sloppy on your feet after constant wear. Certainly take a fave pair with you, but check online with, say, Zappos.com or planet shoes.com to find other shoes with the features you like that could give you additional support. Let me emphasize "lightweight" here. It sounds like you'll be on an extended slog-you'll be glad you brought another shoe option.