Norwich has little or no traffic if you don't count the North Sea helicopters.
Which probably means, in an ideal world, an extremely good chance of getting a clearance! It shouldn't be any more difficult than passing through the ATZ of Cambridge, for example.
I learnt to fly in Florida and haven't had any issues with transitioning Class D, C or B airspace out there. It is nice to have controllers give you traffic information or separate you from other aircraft in busier areas. But then their infrastructure is centrally funded.