BSA (the optics and air rifle manufacturer) doesn't make AR lowers that I'm aware of. My google-fu is also failing to find any association between "BSA" and "AR" at the moment.

BCM does sell upper halves separately, however. I would suggest that there's a possibility that your lower is a mutt and your upper is BCM. Not that a mutt gun can't shoot, but it leaves you wondering what parts are in the guts of your lower?

Where is your upper marked "BCM"?

Caveat Emptor - "Let the buyer beware"