I think the prohibition technically isn't against Nazi flags but against the symbols of unconstitutional organizations in general. It goes back to the ban of the West-German Communist party in the fifties, though it does mostly seem to apply to Nazis now because nobody cares about communists anymore. There's also a law against holocaust denial and something along the lines of "incitement of racial hatred", which also often affect Nazis.

And while I don't necessarily think we should have these laws anymore, they did get written in the decades immediately following WWII, and how the hell would you go about getting rid of them? Imagine what kind of message it would send to Nazis, and anti-semites in general, if politicians started working on something like that.

Anyway, I can't speak for the UK but how often do people really get arrested for Nazi shit in Germany? I see a headline from time to time but it's mostly about violent crimes.