If you have nothing on the socket area then that butt stock isn't legit, flat out. All No4T rifles that went through Holland & Holland, whether they passed muster or not, would have had the stocks serial numbered in those specific locations, they would still be clear and visible to this day. If you don't have those markings, there is no way that stock is original to the rifle.
Can you post detailed pics of the top of the butt stock near the receiver, and the socket itself when removed? At best the butt stock may be a replacement, even if the fore-end is original. Also, I can see clearly that the heel does not bear the S51 mark where it should be so, it really is no dice on the butt.