Backworth Bob,
Other than the proof marks applicable to the allowable proof diameter range [measured 9 inches from the breech face],chamber length and if appropriate the word," choke," U.K. proof houses add no other marks concerning the barrel dimensions. It is the gun makers responsibility to ensure that the barrel wall thickness is sufficient to accommodate resultant proof stress and if applicable any recessed chokes[back bored].
A word of caution is perhaps in order. Back boring English guns greater than the maximum diameter allowed under the rules of proof renders them, "out of proof" and subject to reproof in the interest of user safety. Under .U.K. law sale of guns out of proof is a serious offense.
