According to the great Wikipedia, "A folk club is a regular event, permanent venue, or section of a venue devoted to folk music and traditional music. Folk clubs were primarily an urban phenomenon of 1960s and 1970s in Great Britain and Ireland, and vital to the second British folk revival, but continue today there and elsewhere".
I see no reference to payment to be a member or to attend the club! The club that consists solely, or mainly, for the purpose of a regular sing around is, in my humble opinion, a Folk Club. They are, with all other "regular events" mentioned in the definition above, the very base from which folk music grows. Elitism is not good, the great range of folk clubs present in the UK is the strength on which folk music relies on to flourish.
Obviously all regular meetings to perform or listen to folk or traditional singing and/or folk or traditional music, must be included in the definition.

Dennis