A lot of gunmakers have used barrels and actions originating in either Spain or Italy for their guns. Your point about marking these origins is a valid one but the answer is 'yes'.
Sourcing components abroad happens in all industries but the firm in the driving seat will brand the product and be seen as the origin of the product, even if not of all the raw materials and rough parts.
Where one draws the line between raw materials and finished component parts is the key. Is a basic Arrietta barreled action which has been stocked and finished in the UK by 'A. Smith' an Arrietta or an 'A. Smith'? A bit like asking is a 1930s Willam Evans a William Evans or a Webley & Scott.
A lot of guns come in almost finished and therefore bear foreign proof marks and are recognizable from their exterior form. Others are filed up significantly in the Uk and jointed and proofed here. They differ significantly from the product that would come from the Italian or Spanish maker but utilise the basic framework.
Again, this is like comparing a Rodgers action Army & Navy plainly finished sidelock with a 'best' finished Beesley built on the same platform. In either case, no mention would be made of the origins, though the Beesley would bear London proof marks and the A&N would bear Birmingham ones.
Beesley certainly would not have put " constructed mostly by workers paid by F. Beesley using components from Birmingham and Wolverhampton and wood from France and partly finished by various London outworkers" on the rib.
Today, The Guerinis that William Evans have turned into their St James model clearly show their origins and so do the Arriettas that Paul Roberts has based his sidelocks on. The Purdey Sporter uses components from Italy but is not an Italian gun.
Sourcing parts and materials continues to be a problem for the British makers. They have used foreign components from long before the 1880s when Purdey started using Belgian damascus tubes.
