It has long occurred to me that this song (Donnybrook not Widdecombe)is one of the most corrupted songs in the folk canon, and a vivid example of how the folk process of oral transmission and improvisation, which usually enhances songs, can occasionally destroy them.

Unless I miss the point entirely, this began as a humerous song. The humour lies in meeting a person with a standard surname, which then unexpectedly turns out to be the end of a longer expression:
Dix    Fiddles Dix/Fiddlesticks
Long   Runner Long/Run-along
Potts Piddlepots

But then people started to miss the idea and added verses which do not work, either because the first word is not a standard surname (Necks/Dirty necks), the second expression is not a standard one, hiding the original (Balls/Bags of balls), or entirely reversed (Rump/Rumpitump).

What you end up with is versions like one collected in East Anglia where the original point has been completely lost in favour of a new one (Necks/Dirty necks, Feet,Dirty feet, Knees, Dirty knees etc. etc.)

I hesitantly guess from the deeper levels of corruption which seem to appear in many East Anglian versions that the song is indeed originally Irish, that it was increasingly corrupted as it travelled across, and that the inhabitants of Silly Suffolk merely tried to localise it by giving it a title such as Barningham Fair. Having been born and bred in Barningham, I recall the occasional fete worse than death, but no Fair.