There are several threads missing here: firstly, like it or not, the National Song Book laid a foundation in Schools which the early clubs drew on. Secondly, both Wales and Northumberland had local community performance traditions which never broke: in Northumberland, the practice of visiting around the farms in the evening, as it was a major exercise to get into town for the cinema. In Wales, the Hwyl Nos and Gymanfa Canu traditions, often based around the Rugby Clubs, which went far beyond the hymns and arias. Maddy Prior's first steps, for example, were taken in a Methodist Church youth group in Kilburn. I was taught maypole dancing in school in the 1960s by one of the "heritage" dancers passing on the family tradition.
Therefore, yes, if you want to focus tightly on the Clubs themselves, you have to go back the jazz/skiffle. But they drew on older roots sown by RVW and CS and their circle in the 1920s, performed in the Church Fayre processions and the like.