As Ian's request is focused on British folk rock, specifically Fairport Convention who seemed to have kicked it off:

Some information here about their first album "Fairport Convention" (Island, 1967): http://www.slipcue.com/music/international/celtic/artists/fairport.html

"...they were trying to be the British version of the Jefferson Airplane, a roots-oriented psychedelic jugband."

Regarding the later Liege and Lief:

"They decided to try out an entirely new approach, foregoing almost all contemporary songwriting in favor of traditional English folk material, which they would play using aggressively modern, electric arrangements."

I think there was a mention in Folk Roots of the first traditional song to hit the pop charts, and it came out of a discussion on uk.music.folk. Can't remember what the song was, but it was circa 1958-ish.

It was inevitable anyway. People take the new instruments and styles and use them for existing songs. I believe Fairport were just the first to do it with Traditional British songs.