Ok, I have created a new thread to enquire about this.
I'm rather fond of the old tune Packington's Pound. It used to be a popular broadside ballad tune before 1700. I was curious to find out if it lasted into modern times.

This is the tune in question:
https://www.jellynote.com/en/sheet-music-tabs/anonymous/packingtons-pound/504a12

Here are three example recordings of old ballads sung to Packington's Pound taken from the University of California English Broadside Ballad Archive:

A Caveat for Cut-purses recording:
https://ebba.english.ucsb.edu/recordings/r2.46-47_Packingtons_Pound.mp3
Transcription:
https://ebba.english.ucsb.edu/ballad/30274/xml

The Royal Victory recording:
https://ebba.english.ucsb.edu/recordings/r3.240-241.mp3
Transcription:
https://ebba.english.ucsb.edu/ballad/31918/xml

Pittie's Lamentation recording:
https://ebba.english.ucsb.edu/recordings/P1.162-163.mp3
Transcription:
https://ebba.english.ucsb.edu/ballad/20071/xml

I really like that website, it is useful when looking up broadside texts and their respective tunes. I think they did a good job with it.
Pittie's Lamentation for the cruelty of this age was also recorded by Ewan MacColl as "Pity's Lamentation" on "Broadside Ballads, Vol. 1 (London: 1600-1700)" (1962).

We already found out in the "Tune Req: Derry Down" thread that the song "Droylsden Wakes" (Roud No. 3290) uses a form of the tune.

Here is a recording of it by Ewan MacColl:
https://www.youtube.com/watch?v=UyonJxPd-Uk

I also posted these scans from Randolph/Legman's Unprintable Ozark Ballads about a bawdy version of Brian O Lin, called "Brinzi O' Flynn" recorded by Sam Eskin in 1942 from a British seaman in San Francisco that used the tune:

Here are the respective pages:
First:
https://i.imgur.com/eiYEX8H.jpg
Second:
https://i.imgur.com/zvvoMjh.jpg
Third:
https://i.imgur.com/weW0AfW.jpg
Last:
https://i.imgur.com/zCihqdI.jpg

There also a second text there, Thumble O'Lynn, also set to the Packington tune.
I have never encountered another Brinzi version apart from the one given in this book. And I don't know of any other songs from oral tradition that used a variant of this old tune.

If anybody happens to know more examples I'd love to hear them.