You do need to file a flight plan to fly through controlled airspace, but what you do if file an abbreviated flightplan by telling atc your intentions, filing a full flightplan over the r/t is a different kettle of fish. When you book out at an airport in class D you are also filing an abbreviated flightplan.
As side note, i have been told to remain clear of controlled airspace in the USA but never in the UK.
Class C airspace is not the same as our class D as IFR must be separated for VFR, not just given traffic information.
The only way to fly in class A airspace in Britain is to fly IFR, though you can fly SVFR through a class A zone, or would not be able to get to the channel islands.