But they were able to setup the core of their commercial and governance infrastructure in the middle of London, with no particular notice from muggles - not to mention, we know that the government already knows about wizards (MoM liaises with the PM). So there must be a quid pro quo already in place, with the government tolerating and aiding in the existence of a semi-independent polity in their heartlands in return for unspecified benefits, probably defence against foreign wizards.