Used to be able to buy a tyre pump that worked off cylinder pressure. You took a spark plug out and screwed this in its place. Still have one, though don't use it. So your BSA runs on one cylinder whilst the other pumps your tyre. Its era is given away by the fact it is threaded 14mm and 18mm to fit engines using either plug sizes. Don't try it on a B series or gold star .......
It has a valve to control flow direction and sufficient breather holes to mitigate pumping your tyres with mixture instead of air.