Jon simply attributes this as “From Carthy. I like the gentle humour of this. As I’ve said before I’m not desperately keen on ‘funny’ songs, but this seems to me more like an Aesop’s fable.”
It certainly has a folklore tale element to it as Martin Carthy’s notes reprinted at Mainly Norfolk allude to. The tale of the argument and refusing to speak is very old and can be traced back to antiquity with the simple moral lesson found is Aesop and so forth. This song as one of the Child collection (#275), is probably of Scottish origin and probably itself very old, but there do seem to be several variations, some undoubtedly English. You may like to try this Mudcat thread too, although it’s mostly about the abiding chauvinism of folk songs, with bad wives more common than bad husbands. I’m sure that’s true, but neither party takes any credit out of this, jolly as it may be.