HW Hyatt has it mostly correct....except.
Any gun made from 1899 to present requires a BATF form 6 prior to export.
Not only will you pay holding and storage costs, you'll wait for 6-8 months for that gun to be approved for import. You'll also need a customs broker and FFL to get the lot out of customs and BATF hell on this end.
On guns made after 1899, the notion of an inefficient market between the UK and US isn't the case. The margins would be extremely tight.
In one example, I saw a nice boxlock for 350 GBP. It needed $250 in stock work to be worth $1600-$1800 here in the states. After calculating all the costs involved, the actual cost was about $1350. Tremendous aggravation for a 10% net profit.
Bottom line, it must be a labor of love to import a gun, not a profit scheme.