There are two governments at work in York, one mostly mundane and one mostly magical. Inner York is run by a primarily mundane government, due to the low concentration of wizards in the area prior to the bombs. Outer York is run by the wizards because many of its refugees come from magical origins. There is some crossover - no one government is entirely comprised of one group or another.
The two governments cooperate with one another and generally speaking, work effectively together. The main difference between governments is in their problems and concerns. Inner York and Outer York work together on issues of law enforcement, sanitation, healthcare, and education.
There are very different levels of support, however, for government-driven initiatives. The Outer York government tends to have a significant amount of support from its populace while Inner York has many dissidents, particularly where it comes to the issue of immigration into the city.
Several grassroots groups have sprung up in- and outside the walls. Among these is a group of would-be educators who want to issue pamphlets and begin trainings so that muggles may learn more about how the wizarding world operates. This idea has met incredible resistance from both sides, however.
In terms of the national scene, Great Britain as a country is no longer what it was. Cities have become their own states, for the most part, and as a result, there is no single unifying force and communication/transportation networks are fairly splintered.
