[Arran]

As long as the plastic sheeting isn't too thick, I think that the thickness of photographic film would be just about right, if you have any strips of that laying around, some PETE plastic used in food packaging would also work. Fortunately it's a small winding so the solenoid probably has more then enough on it's bobbin, if the gauge is the same. On an antenna coil it's not really that critical, on an oscillator coil the gauge, and number of turns is critical. Usually when I find a bad antenna coil, and this has happened more then once on a battery radio, it's because of a lightning strike, and the coil is burned to a crisp, they are also typically smaller on sets from the 1940s.
Regards
Arran