Not sure what the situation in the UK is, but in NL we can get a 'gun passport'. I just dug it out... apparently it is a "European fire arms passport', that declares that, I am lawfully entitled to own and transport an Air Arms NJR serial 1336, and a Weihrauch HW97k serial 1445920 within the EU.
Since this is apparently a European affair, it looks like you guys could get that too.
Lemme do some Googling...
... ah, here it is:
Does this help you guys?
The Filthy Pig
: Air Arms 100 (1990) + AA Olympic trigger + Welham reg + Custom Shop CS1000 stock. Status: leaking.
The Unknown Quantity
: AA EV2 Mk4. + BSA Platinum 10-50x60 + Jon Harris wheel. Status: sorted up to 25 yds.
The Limping Dog
: Air Arms Shamal (1989) + unknown origin sporter stock + Optisan Cobra 3-9x42. Status: slowly leaking; needs work.
: HW97k + Venom Lazaglide. Status: working just fine; needs scope.
with apologies to NJR100