Marking on 1917 BSA SMLE.

Picked up a 1917 BSA MkIII* this weekend, * has been crossed out, Indian service afterwards, left side of buttsocket reads 'RFI 1929'. My question concerns a marking on top of the knoxform and left side of barrel along with all the usual proof marks. The top of the knoxform is a small 'star' over a W. Marking is also on left side of barrel but bigger. 'star' over a larger W. Any clue?

Probably an arsenal inspection mark related to the 1929 FTR, especially if the barrel is original or at least pre-1929. Post some photos - might be other clues we can see.