Craig. All guns submitted to British Proof are currently recorded. The Proof houses are exempt in British law of any licence themselves. 30 years ago I took guns to proof and was never asked for any authority to posses. But things have changed ,thanks to stupid politicians, so I would assume that all guns submitted privately would need to be licenced. All guns submitted by the trade would need to be on an RFD licence.
Reciprocal proof arrangements have been in operation for years ,the main criteria was that one country would recognise the proof of another if it had a state controlled proof or a proof house run under Government statute. This was prior to the current CIP arrangement. Thus a gun proofed in Italy for example would have its proof status recognised by the US [if the US had proof houses run under Fedral statute] and vice versa.No need to reproof unless necessary for what ever reason.