Can a scope be fitted and are spare parts still available? The serial number is S 12040.
BSA STANDARD AIR RIFLE
Your rifle was despatched in October 1922 and seems to have had a hard life.
When manufactured it was not intended to be used with a telescopic sight, though I have seen scopes fitted to this model, nearly all of which have considerably reduced the value of these classic rifles.
However, if you wish to have a telescopic sight fitted, this should be carried out by a competent gunsmith.
Your rifle is not performing to your expectations for several reasons.
A spring and washer replacement would definitely be beneficial as would a general overhaul, cleaning and lubrication.
You should also check that you are using correct pellets. Only those of 5.6mm diameter will work efficiently in your rifle.
If you can manage to use the rifle without the addition of a modern scope, it will retain its collectable value.
A scope does not make an air rifle any more accurate, but provides a means of being able to see a target more clearly.
Spares are still available for this rifle.