Arbe,
What you have there is a BSA 'Standard' No 1 Bore (.177) Air rifle in Light or Ladies Pattern. It is an underlever model with a push button end to the cocking lever under the barrel. This was a new model made by BSA,which took over from their previous model (The Improved Model D) in 1919.I would say that your rifle was probably made in early 1920 and would have cost 4 pounds,0 shillings,0 pence. Which was around a months wages for an unskilled worker. So they were very expensive at the time.
That style of gun was originally designed by a man called George Lincoln Jeffries, in around 1905.First made by him, it was later made by BSA, who eventually bought all rights to the design and made the guns up until 1939, and the outbreak of world war two.
Along with the small .177 light pattern, there was a bigger .22 sporting pattern, which was 45.5 inches long and a lot more powerful for vermin shooting .
There rifles are classics and a lot more accurate that most people realise. Your rifle should have a two hole trigger block, with the weight of the trigger set by the factory. A few years later BSA designed an adjustable trigger mechanism, which was housed in a three hole trigger block.
All in all you have a classic airgun, which could be valued at between 120 and 150 quid in average to good order (all original parts with some bluing) really good to mint ones are around 200-250 quid.
Hope that info helps
ATB
Lakey