Question about barrel on recently purchased Lee Enfield?

Bought this enfield last week and have been having some questions about the barrel and was wondeering if you or anyone could help. Concerened about some markings under the wood. Are their serial numbers under the wood line? I have one by the breach but with out the (K) in front of the number 38735 as is on the breech. It also has the Biringham Nitro Proof mark on it as well as on the right hand side of the breach Government prrof/44/broad arrow. Does this mean that the barrel weea made in 44? Sorry for these questions but from dealing with civil war guns you can imagine my skeptism about a Sniper being correct. Breach also has year 1944/England on it as well as the scope.....

Thanks for any help.

Usually S/N is above the wood line when the handguard is removed, but not always. Pictures are your friend when determining whether these rifles are "correct" or no. Saves TONS of speculation and guessing.

Thank you for your response...Have you ever seen British prrof mark above a date(44) over Broad Arrow on the right side of the breech under the forstock?

If by the right side, you mean the bolt handle side, the two digit year stamp is often found there. If you have a No4(T), feel free to post photos and we'll all chip in with our opinions! ;)