Sorry, I should have worded my post differently, I said it looks like a B3, not that it is a B3. There would be no BSA markings on a B3, so if it says BSA, it probably is one.
I should have said, "the B3 looks similar to your gun".
CZ, Your rifle is most likely (according to pictures in "The Airgun Book" and Smith's "Gas, Air and Spring Guns"), a Barvaria S54 Standard. There were 3 variants of the Series 54, standard (single "grasping" grove on forend), the sport with deepend forend and three groves and the match, which was basically the same as the sport with a muzzle wieght.
The BSF- Bavaria rifles are good quality German made rifles, I am surprised some of the ballies on the forum didn't know the BSF's, I meen Guido is 94 and Gerrief, well he just carries his age well (he he).
I'll sort you out when I see again for calling a "Ballie." (Although I know I am.) I grew up with Diana,Gecado(?), BSA,Falc(?) 80 and 90 and the the Jelly. Never heard of a BSF. For a long time in my life I did not bother with toys like air rifles. Today I'm sorry because my best shooting days are gone, never realised it.
Ja swaer, those were the days spending weekends on Oupa's farm, BSF in the hand and a mouthfull of Marksmans. Taking our jobs of controlling the kwazilion doves raiding the sunflower lands seriously was exausting! %-6
Many a Monday I had a burning backside from not staying awake in class.. :sleepgo