The hole was bored out round then a plug fitted and BSA did that when they did the conversion back in the early 1950's. This is a BSA commercial conversion. Someone wrecked the original stock and the barrel was a sewar pipe. I have owned it for years but about 5 or 6 years ago we got a new BSA made barrel from Knibbs and it was fittied by a gunsmith in Yorkshire. This Parker-Hale modified stock was one that I had laying around so until we can get some thing more in keeping it will do. The bore is mirror bright and has been Ball Burnished by Parkers.

There is no welding the plug is either sweated in or silver soldered in place:-

You can just make out the round mark of the plug. I will see if I can get a better photo of this and also get one from the BSA Model E as I still own another that has it's original BSA stock fitted.

Hope that helps.