Most of the lyrics were made up individually for each programme and were based on topical subjects of the day. Hence your one about rationing. There can't be many examples available, but the words used for one programme can be found here. (Scroll down).
There's also a complete broadcast of a single episode of 'Much Binding' available online here. (Be warned - It's an exceptionally scratchy recording!).
I remember listening to the programme as a child and for some reason can only quote one of the other ditties that were sung. They always started, "Down in jungle, chanting every day, you can hear the natives all say; (then) down in the jungle, living in a tent, better than a pre-fab, no rent!"