I don't want to say "that should be easy to do," but I'd be shell-shocked if any company with experience doing navigation systems couldn't figure this out without too much trouble.

Also, even if GPS signals are hard to get in London, navigation in a fixed city can be calculated in lots of different ways. Allowing for some regulatory limits, a company (or an experienced third-party) could scatter their own transmitters around the city as needed, figuring out which frequencies give the best accuracy.