You only need to discuss export with a dealer that specializes in import/export. Champlin Arms, British Sporting Arms, and Cabelas are all good at this process. They do charge a fee, though this is the safest way to do it without alot of hassles.

Would this restrict rifle sales to within the country??

No.

Would Doubles just be sold out of various gunshops or are any sold on the net or at auction in the UK??

Not certain what your trying to say here. Guns are sold through gunshops, the internet, through private auctions, and private sales between individuals.