Just out of curiosity, are foreign registered planes / foreign pilots / foreign-licenced pilots, or any combination thereof, expected to jump through those same hoops?
LH2, what you need to understand is that with international flights you are normally expected to fly from a customs/immigration airport to a customs/immigration airport. At these airports your passports are checked, you have the ability to declare goods etc. This is regardless of the registration of your plane, passport or license.
The GAR form is a unique UK thing: By filling it in and faxing it to the proper authorities with sufficient prior notice (all depending on where you are coming from/going to; the details are on the back of the form) you can essentially fly from any UK airfield to foreign, or from foreign to any UK airfield. Obviously only if you have no goods to declare, and subject to a few other reasonable restrictions.
So the GAR form, despite the challenge of figuring out where and when to fax it to, is designed to make things simpler, not more complicated. And in fact, it can be very simple: just phone up the UK airfield involved (usually PPR anyway), tell them the GAR form is on the way to them via fax, and ask them to forward it to the proper authorities for their field.
And yes, the GAR form and its associated liberties can be used by foreign registrations, passports and license holders too.
At the other end of your trip, usually mainland Europe, Ireland or some small island like Jersey or IOM, your first or last port of call should still be a customs airfield. I don't know of any GAR-form-like mechanisms within Europe or Ireland.
And of course, once you're inside the EU/Schengen region, you're free to fly from any field to another. (Countries that are in the Schengen region but not in the EU, or vice versa, are a slightly more complicated matter.)