Looks a like a fun rifle to shoot---congrats!

It is not a factory sporter. As darwinmauser said above, the royal cipher indicates that this was a military rifle, converted privately by a gunsmith. It is possible that the conversion was done by Parker Hale, because they offered some conversions that look similar to yours, although the buttstock is quite different. (PH also sold BSA factory sporters, but this is not one of those).

What is the overall length?
The barrel length?
Are there any Parker Hale markings?

More photos and details on all the markings will tell us much.

As far as I know, BSA never performed conversions of military rifles or offered any for sale. You may sometimes encounter BSA factory sporters with military barrels, but those were fitted privately--not by BSA.