Yes those serial numbers would be correct. The .22 would be a very early BSA "Standard" (Long or sporting pattern) made in 1919. I would think it would have a two hole trigger block (meaning that the factory set the trigger pull which was non-adjustable) If you look where the rear of the trigger guard touches the underside of the stock, you should be able to make out a small stamp in the woodwork. In the centre of this triangle there would have been the trigger weight stamped in (eg 4LB)
The second .177 is the "Club Standard" which was a full length Target gun. They were made at the same time as the "Standards" so to differentiate production they added the second prefix letter 'C' so they became 'CS' models. Yours would have been made anytime from around 1921 to 1933ish.
Both guns sound right to me. Both would have cost the equivalent of at least 4 weeks adult wages when bought.
Lakey