Brit is a perfectly acceptable term to use when reffering to a British person. Don't see why anyone would take offence at that.
Firearms and ammunition can be bought from RFDs (Registered Firearms Dealers). There are maybe half a dozen within 30 minutes drive from my house. Shotgun ammunition is not controlled at all in many parts of the country, however.
These shops are usually dedicated gun shops, though some of them will often have airguns and hunting equipment such as decoys too. There is also the odd shop which does fishing and guns.
They are usually small, independent dealers. I think you would call them 'mom and pop' stores. However, there are a couple of fairly large mail order dealers such as Litts. When you order of the internet, by phone or mail etc, the order is never sent directly to you. It is sent to the nearest RFD who will hold it for you until you pick it up. When you pick it up, you must show yout firearms or shotgun certificate (whichever is appropriate to the item).
I have never seen a sports shop that sells firearms or ammunition. Supermarkets do not sell firearms or ammunition.
Private transfers are a bit of a grey area. Usually, you will put your gun up for sale with an RFD. It works a little like eBay usually. They sell it for you, you get the profits minus a small fee from the RFD.
Oh, I forgot to mention 'russiangear.com' or something like that. They are an army surplas store mainly, but also sell some SAIGA rifles.