Sorry guys, but there are too many fire side lawyers on this thread.
I respectfully suggest that some/all of you acquaint yourselves with the terms of the Firearms Act (1968).
http://www.legislation.gov.uk/ukpga/1968/27
The relevant sections of which are 47 (Powers of Constable to Stop and Search) an 48 (Production of Certificates)
Sorry to diappoint some of our more vociferous contributors but,
A PHOTOCOPY IS NOT A VALID FAC, not in the eyes of the law and not in the eyes of a grumpy Police Constable with the law on his side, not yours.
If you are in possession of a firearm or firearms, and a Police Constable (or rank senior to Constable) asks to inspect your FAC which authorises your possession of said firearm/firearms, you MUST IMMEDIATELY produce the FAC. Failure to do so is a specific offence under the terms of the Firearms Act, wanting to keep your FAC pristine or fear of losing it in the field IS NOT an acceptable excuse, in fact there is no excuse at all for failure to produce your FAC (the original) ON DEMAND.
I emphasise, the law gives no specific authorisation for use of photocopy!
Of course, individual Police discretion is allowed, as in all cases of Police dealing with the public, so a Police Constable (or other rank) may, subject to their own discretion/pre-disposition/judgement, accept a photocopy or notarised copy, AND although the law doesn't give a specific right to produce a photocopy, it also does not specifically ban it, but do you want to throw yourself upon the mercy of a cop whom you might not know?
The said Police Constable can, and is fully entitled to under the provisions of the Firearms Act;
1) sieze the firearm(s)
2) detain the holder of such firearm(s) until satisfied that the terms of the Firearms Act have been satisfied.
Now, as an ex-cop I have to tell you, indeed warn you, that the very worst thing that you can ever do when dealing with the law is to take the high horse when you don't have a saddle.
If you can't prove that you have authority to carry a firearm, and sorry guys but an actual, original, signed legible FAC is the ONLY valid proof you will ever have in your possession, then you are liable to questions, possible arrest and maybe even siezure/forfeiture of your firearms.
In short, carry your FAC, it's easy and I do it all the time with no trouble to me at all. The FAC fits nicely into a waterproof wallet, such as you can buy for protecting documents, mobiles or cash whilst kayaking and such.
It avoids any unnecessary hassle with the law and the possibility, however remote, of arrest and confiscation of my prized firearms. If you wanna risk carrying your firearms without also being in possession of your original FAC, you best hope that the cop you meet knows you OR bite your tongue and hope you get the chance to explain AND the cop believes you.
Sure, get all mouthy and tell the cop that you know your rights and that you "know his job better than he does", but I would suggest that you better learn how to like the back of a Police-car and how to manage without your firearms pretty darn sharpish.
Believe me, if your firearms are ever siezed, for whatever reason, it's gonna count against you in future dealings with your Firearms Enquiry team (FET) or FEO.
But hey, this is just my advice, with some knowledge of the law and experience of how to enforce it, you do as you feel happy with but don't be surprised if you come a cropper when/if you don't follow the letter of the law.