Yes. The purpose of the import markings established by the GCA of 1968 was to make it possible to do a gun trace. For example a surplus firearm is found at a crime scene - authorities go directly to the importer with the make, model and S/N - the importer gives up the dealer, who in turn gives up the first purchaser.
A mark which just states "England" or "English Made" would serve little purpose as far as a trace is concerned.
There may well be some other statutes or regulations that require products to be marked as to country of origin.