Plains99,
Those CF2 BSA's usually shoot extremely well, as you have found with yours.
They are strong and accurate rifles for sure.
I started my kangaroo shooting career in the late seventies with a CF2 in .243 Win.
A couple of years later I bought one in .270 Win and both those rifles shot very well and the.243 held up to the rigors of pro shooting with no problems.
A mate had one in .222 Rem and we used to shoot all sorts of varmints at long range with it.

Thesedays the BSA rifles still turn up for sale from time to time, but they are by no means common on the Aussie market, especially the early controlled feed models from the 50's.
I've owned and used quite a few of the early controlled feed BSA rifles over the years and still use a couple thesedays.

All the CF2's I've seen were checkered, so maybe the stock has been sanded down at some time?
Checkering on CF2's was usually of the basket-weave style.

That rifle should serve you well!