Peter Pilbeam told me in 1977 that he had several hundred hours of Folkweave programmes on tape. I don't know whether they were his personal copies or in some BBC centre, but they did exist. If I remember correctly, FW was produced someplace outside of London, so they probably weren't lost in some mad cleanup at Broadcasting House.

Do any of the 1950's "Blues and Ballads" (or was it "Ballads and Blues"?) programmes still exist?

I have a copy of "Bold Nelson's Praise", the program that Bert Lloyd put together for the anniversary of Trafalgar. On BBC Transcription Service discs.