It is illegal to export from the UK any arm that is out of proof or unproofed . The law applies to all firearms including antiques ,whether they be flint locks or other .
Back in the 70's Webley made some single barrel martini actiond shot guns in .310 [I think] for an American company ,could have been Winchester .The idea was to have "indoor " clay shootig galleries . They were not proofed at request of the US customer and I do recall ther was a problem with export even back then .