The Ballads & Blues club,The Good Earth, & The Topic all seem to have a claim but going back to points made by LesInChorlton & GuestFidjit - The Chris Barber band released an L.P. in 1954 featuring a couple of "Joke" songs by their Banjo player who was then known as Tony Donnegan the style of playing was called "Skiffle" & it became immensely popular,Britain was Tory-governed for 13 long years from June 1951 onwards,Frankie Laine & Mantovani dominated popular music,Teddy boys (Britain's first major youth culture) were commonplace from cica 1955 onwards,Suez & Hungary both happened in 1956 & reaction to this helped create what would become the New Left. In July 1957 amateur skiffler John Lennon first met wannabe amateur skiffler Paul McCartney & in 1958 C.N.D. was formed.If you believe,as I do,that musical traditions are not invented but evolve you might see all of these things as being little streams that fed the big river that is contemporary folk.