In the case of a flight to the CI/Ireland/ION, the Plod do however normally phone you, often in the middle of the night, with a "permission number".
Just to point out that this isn't uniform across police forces. Many seem to just ignore the fax (or probably correctly realise that you've met your obligations and don't need any permission number).
So if you don't get a phone call with a permission number, don't be too worried about that.
I've never received such a call, but have come across one force (North Wales) who for some reason expected me to call them looking for the number!
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.
This is not something that I would do. The obligation to notify your flight rests with you, not the airport.
If someone forgets to do it, or the airport claims they never received your fax (eg. machine out of paper, and someone stupidly resets the memory first instead of checking the paper) then it's you that comes into question.
Saying that you faxed it to the airport, won't really cut any ice with the authorities, because a) the airport may deny ever receiving it, and b) it's your obligation.
Having had the "please call special branch" call given to me by ground ops on arrival, and then received a lecture for not notifying my flight, I was very happy to be able to politely inform SB, that not only had I notified my flight within the proper time scales, but I also had a fax confirmation page (with me) that could prove that they received it.
If you fly regularly with these flights, then it's a matter of "when" you get questioned by SB rather than "if", even though you've done everything correct. I always have my fax confirmation page with me now.
dp