A lovely rifle, It looks like the No 1 Pattern as per the 1908 BSA catalogue. AS you have no doubt discovered, they have a great feel, very pointable, like a well made shotgun.
I have a no 2 Pattern BSA with a shotgun style safety in similar condition to yours and a BSA No 4 Sporting carbine style Lee Speed that has the safety like yours but has a charger bridge fitted. It has seen plenty of work, but still has an excellent bore and shoots very well. The stories they could tell.