Dick Holdstock calls it "The Bold Fusilier." Here's his 1988 performance with Allan MacLeod. I've heard them sing it many times.

https://www.youtube.com/watch?v=FOVQWjW-R64

Dick's notes:
Dick Holdstock of (Holdstock and Macleod) sings an early 1700s song about army recruitment in Rochester Kent, for the Marlborough Wars. Pete Coe chose the melody for Waltzing Matililda for this partial Broadside Ballad. Recorded at KIXE Redding in 1988 on Stage 9.