Hi there
I think one should always be cautious when dealing with the US and especially cautious of the application of ITAR regs.
Category I—Firearms, Close Assault Weapons and Combat Shotguns
*(a) Nonautomatic and semi-automatic firearms to caliber .50 inclusive (12.7 mm).
*(b) Fully automatic firearms to .50 caliber inclusive (12.7 mm).
*(c) Firearms or other weapons (e.g. insurgency-counterinsurgency, close assault weapons systems) having a special military application regardless of caliber.
*(d) Combat shotguns. This includes any shotgun with a barrel length less than 18 inches.
*(e) Silencers, mufflers, sound and flash suppressors for the articles in (a) through (d) of this category and their specifically designed, modified or adapted components and parts.
(f) Riflescopes manufactured to military specifications (See category XII(c) for controls on night sighting devices.)
*(g) Barrels, cylinders, receivers (frames) or complete breech mechanisms for the articles in paragraphs (a) through (d) of this category.
(h) Components, parts, accessories and attachments for the articles in paragraphs (a) through (g) of this category.
(Taken from the Code of Federal regulation ITAR part 121 The United States Munitions List)
Section h is a broad category but covers pretty much any weapon we might want to legitimately use under the 'nonautomatic' (a lovely catch all that grabs bolt actions, falling block, doubles etc) and semi automatic subsection. The debate is usually around whether the item in question is legitimately materiel (not a spelling mistake) or not. I think it's been a while since a double rifle in 30-06 would be consider materiel but, on the face of the definitions, it's a non automatic firearm of less than 50cal so it's technically covered.
Legitimate imports will have the necessary supporting approvals hence we can buy US guns, bullets and accessories that would be covered and restricted by 121 in the UK. Importing by other means will not. As far as I'm aware, there is no quantity threshold so a single unit is viewed under the regs in the same way as 50 units. Stuff will always get through - no system or legislative instrument is perfect - but, like speeding, there is a consequence in law if you get caught.
Not a definitive answer by any means but hopefully in some way useful.
FN