The first question is if the bike has a freewheel or a fixed gear cog the bike is too old to have a freehub (which has the mechanism which allows the wheel to turn without the pedals turning (i.e. freewheeling) inside the hub; these were ~1980s).
A fixed gear just threads on the hub and will allow you to make the wheel turn if you pedal forwards or backwards. A freewheel allows you to freewheel; theres a ratchet that allows you to keep the pedals stationary/pedal backwards without engaging the rear wheel, yet you can pedal forwards and engage the rear wheel.
Not all bikes with one cog have freewheels; some of them have fixed gear.
If the bike has a fixed gear and is allowing you to turn the wheel when pedaling both ways, that is normal (and should be the only type of motion possible).
If the bike has a freewheel: When the ratcheting mechanism breaks in a freewheel, it normally doesn't engage the rear wheel at all; you pedal forward and backward and nothing happens. However, if the ratcheting mechanism gets stuck in the right way (rust, jammed, someone forced it to get stuck, etc.), it can effectively act as a fixed gear. Freewheels became common slightly after 1900, so its fairly reasonable that it had a freewheel.
If the freewheel is acting up (or you have a fixed and you want to have freewheeling), normally I'd suggest replacing it with a new freewheel which may have to destroy the existing one to remove it. However, with the age of the bike, I'm not sure if the existing standards match what was available in the 1940s where you are. You could try spraying in some WD-40 or a lubricant (which WD-40 is not) at the cog and seeing if it loosens up and starts freewheeling. Or, just leave it.