Jean Ritchie recorded a version with something like your chorus:

Tally-Ho, Tally-Ho, pursue him!
The huntsman loudly cried.
A-Hi-Li, A-Hi-Lo
And a down the woods we glide

It was on Marching Across the Green Grass and other American Children Game Songs and you can get the pdf of the notes here: Folkways Liner Notes FW07702 (pdf). She calls it All Ye Jolly Huntsmen and has only 2 verses (blacksmith and miller). She says she heard her first version from a chambermaid in Dublin, but the song has changed by herself and her family.


Searches on the line "Tally-ho, tally-ho, pursue him" come up with 2 sources Popular Song Index - Patricia Pate Havlice. There's no view at archive.org for the entry, but the book can be borrowed from there. The other is for Shropshire Folklore - A Sheaf of Gleanings in a 2018 reprint. A couple of the original volumes are are archive but they don't seem to have the song.


Mick