Do the Wurzels count as a folk group?

Yes, IMO, but hardly a 'little known' one, even in the 1960s, when Adge Cutler was still their leader. They reached the British Top 40 pop charts with "Drink Up Thy Zider" in 1967.

(Of course the Wurzels became even more well-known in the 1970s, after Adge's sad demise, and topped the UK charts with "Combine Harvester", a parody of Melanie's Brand New Key, written by Irishman Brendan O'Shaughnessy.)