Up until quite recently the BBC was the only broadcaster of anything at all inside the UK, although broadcasts from Ireland or other European countries could be received.
There were some occasional folk song broadcasts (but not usually by traditional performers) from regional BBC stations in the 1930's - BBC Northern Region produced a series of 'Folk Songs of the North' in 1933 which included performances by Tom Clough on the Northumbrian smallpipes. There were some recordings made of singers such as Phil Tanner in 1937, singers at the Eel's Foot in Eastbridge, Suffolk in 1939, and Louie Hooper in 1942. In 1949 Jim Copper heard somebody sing How Pleasant and Delightful on the Country Magazine programme so he wrote to the BBC to tell then they'd got the song wrong which led to Francis Collinson broadcasting the Coppers in 1950 on Country Magazine.

A very interesting topic; good luck with your research.

Matthew Edwards