My two cents is that I first heard this particular recording more than forty years ago, and I too found it cringe-worthy. Not because of the accent but because of the intonation and exacessive nasality. I didn't find it funny because I obviously have no sense of humor.

My stupid guess is that MacColl was trying to imitate the delivery of a particular individual, or of the "sort" of individual that he imagined singing the song: maybe a very old man with a creaky voice reminiscing in a very rustic accent. Bad choice.

But finding the track annoying without being intentionally or unintentionally amusing, I see no need to comment further. BFD.