It may have been a wire recording, the BBC had a lot of wire recorders in WWII.
I know that aircraft of 100 Group did make audio recordings in flight of German fighter controllers and then play them back later that night to confuse the Germans.
So it was done, and therefore it can't be ruled out that this recording was technically possible.
We also have not answered the biggest question. If it is a fake, then who and why ?
We have not proved it is a fake, but we cannot prove it is authentic either.
Wire recorders Notice that thousands were made before during the war.
Wire recording conversion Its a trivial thing to get a wire recording digitised