How funny....I know this rifle.... does it have two holes drilled in the top that have been filled in? PM me and I'll guess the serial number for you. If you plan on keeping it, I'll pass along a story or two about its history that you might someday want to pass on along with it.
For now, I can tell you that it was originally a pre-1914 No 1 Pattern Lee-Speed (the highest grade--evident from the engraving), but was rebarrelled with a military barrel (hence the broad arrow and '25 stamp). Original barrel was probably shot out. If you want to see what this rifle looked like when it was new, see Skennerton, page 112.
The buttstock is from an original commercial BSA sporter, but not original to that particular rifle---it most likely came from a 1920s era commercial Lee from BSA (which today is rare in itself), and the BSA patent safety was re-fitted to it. Someone went to some trouble to do that---not sure what happened to the original butt, but the receiver is cut with a slot to accommodate that safety. They also took the trouble to refit the original express sights to the replacement barrel. On the original barrel, the sling eye was located there (on the barrel)...when it was rebarrelled, they had to drill a hole in the fore-end and fit the sling eye there (similar to the way it was fitted on 1920s-era commercial Lee sporters).
My guess when I first examined this rifle years ago (in person) was that some owner was fond of it (who knows what adventures it was part of, in the far off places of the world), and made the effort to keep the rifle going by saving the original bits (safety, express sights) and refitting them to replacement parts when required...he obtained the best available replacement parts he could get hold of. He probably put a scope on it at some point. Also, it appears to be refinished, which again is evidence that someone liked this rifle enough to put work into it. A bubba job is what we call it when someone tries to save some money by using a handsaw in the garage---this rifle is not like that; on the contrary, someone sent some money to keep this old bird going. This was a rifle that got used in the field, I'm sure of it. I estimate that most of this work (probably all of it) was probably done in the 1920s or 30s, because the BSA butt stock would have been hard to obtain after that. The fore-end wood is original to the rifle (although it has more recently been polished up, you can still tell that the wood on fore-end and butt do not match).
So, not totally original, but still a nice commercial sporter; it looks better in person than it does in photos. Very handy and appealing. I know what you mean when you say it balances and feels RIGHT---felt the same way to me.