I'm not necessarily saying that it isn't a genuine T that has been mucked about with & then put back together again - it might be. However, the TR on the butt socket is not what i would have expected to find, & it bears serifs anyway, which is not 'right' even for a BSA Shirley rifle - though perhaps a jealous armourer might have thought it appropriate to add them after the event, perhaps.
The pads are original, but they have clearly been off, & in my opinion are probably off another rifle, having been subsequently fitted to this rifle. Note the file marks across the rear pad screws where they have been flatted off (photo 2). Note in photo 4 also that there is a 'ding' about a third of the way across the top surface of the rear pad, which is not evident at all on the adjacent receiver side wall.
The wood has been sanded & the rifle serial stamped into the forend looks to be stamped upside down compared to others that I have seen (which are 'the right way up' with the rifle held muzzle end to the left).
The bolt handle looks to have been filed at some point.
Safety is a LB (though only a trivial matter).
Style of font of the rifle number on bracket looks different to others I have seen......?somewhat more recent?
Bracket & scope look nice though, otherwise.
There are no doubt various other points that could be made.....but these are a few to start off with.
ATB.