I have a VERY similar 44 BSA Less T No4 to you, also in it's chest. It's in great condition as well. The markings are pretty much exactly the same, pads staked the same, alloy butt plate, same finish to the wood. The action has a thicker coating on it, the carbanised looking type, Brunofix I believe it's called, can't see the action side markings on mine. My front band is not the pressed style as yours is but is the same manufacturer! it looks like you have a solid type foresight block band as do I which SEAMS to be a feature of these 44 BSA T's (I found that bit of info in a previous thread on this site) in fact pretty much everything I know about the BSA Less T came from here, it's a slog trawling old threads but very rewarding.
I've even got the ENGLAND import stamp on the breech like yours so I guess mine had a holiday in the States years ago.
Thanks for your post, nice to see another one of these uncommon rifles and FWIW I think your rifle is spot on original