For everyone on this thread with a historic 303 -
Do you have it with open conditions on your ticket, or is it conditioned for target only?
I have a SMLE 303 which is conditioned for target only. All my other rifles, including a .300, are open. The FEO explained this as they don't really want people going hunting with 100+ year old rifles when they own modern rifles as well.
FYI OP - non FMJ 303 British hunting ammo is not that common in the UK. Easy to find in Australia or Canada, but not so easy in the UK. I see you have found some Winchester and Federal SP rounds, but that isn't the kind of stuff I see much of at the average UK gun shop.