The gun would date from the early 20's. I don't believe BSA's appeared until after WWI. And after 1925, the proofmarks would have included chamber length--which is absent on this one. So that gives a pretty narrow range of dates.

The "choke" on both barrel flats means that both barrels originally had SOME choke, but it could be relatively little. Like as little as .008, or a somewhat open IC--or even a bit less than that, if the maker so requested from the proofhouse. As Kem says, the only way to know for sure is to measure. And that's true even when you have specific choke markings on barrels. You never know whether someone might have changed them.