Dan Worrall's article includes at least one reference to hymns being accompanied, and also (p23) a comic song. On p36 he presents a table of the different musical uses of concertinas, that includes a number of instances of song accompaniments.

I suspect you're right, Stanron, that the concertina wasn't commonly used to accompany the kind of songs Cecil Sharp would have called 'folk'. Peter Kennedy's book 'Folksongs of Britain and Ireland' includes a photo of one William Rew holding an anglo, but all the evidence seems to be that he used it for playing dance music.