First, you will need to get a UK shotgun certificate in order to shoot a gun at all. One type entitles you to carry, one to acquire. Someone will need to get a UK export license for the gun. This is granted for a specific gun and requires submission of the US import permit for that gun plus a wonderful undertaking that the gun has no CBN capabilities and that you will not transmit the gun to anyone on the embargo list like Iraq, where they were badly in need of Purdeys last time I looked. The easiest thing is to have the gun exported by someone with an open UK license. The exporter ships to your importer and, a few customs and shipping fees later, you've got your gun. Simplest thing to do is buy the gun from someone who does export all the time. They'll already have the mechanisms in place.