[Arran]

There was a really good plan I linked to before that involved using a relatively inexpensive mains operated transformer that you can get anywhere, it had two secondaries which is useful. I have a fairly large collection of 1930s and 40s tube battery radios compared to most people, being a teenager, back in Alberta, they were a way for me to get into pre war radios with very little money, and most of the time I could get them to play without having to do much to them. Unless the 40-81 was stored in an unheated environment it may have still worked without doing anything to it, aside from the rotten battery cable.
I also have a 40-81 somewhere, but the back is missing, I suspect that the A-B pack that was in it may have leaked as there is a patch of corrosion on the rear apron of the chassis. It's likely that the back was damaged as well and throw away, these sets are sort of weird for a portable in that the batteries were stored in the rear rather then in their own compartment under the chassis. These would be a good entry level set for a newcomer to tube radios to work on, I think that there are only 4 paper caps in the thing, and one electrolytic.
Regards
Arran