[dwilt]

Some recordings may be found here:
https://archive.org/details/OldTimeRadio-1940s

(be sure to read first comment which explains how to listen to these, just clicking doesn't seem to work)

"Little of the BBC's radio output of the 1940s has survived, as most shows were broadcast live and were not recorded. The 78 rpm disk recording technology, which was all that was available prior to the development of tape recording, resulted in sound quality that was significantly worse than a live broadcast, so it was better not to fill the air-time with recordings, and being a non-commercial broadcaster the BBC had no financial incentive to preserve its output."

Link to the book: Radio Fun 0144