To be a bit more precise any variant would need to have that characteristic leap on the last note of the 3rd line and the descending sequence in the 4th line, and have something much closer to the usual refrain. O'Rourke has none of this.

Phil Tanner's Henry Martin has none of these and is even in a different rhythm/format to anapestic tetrameter which has been part of this tradition for over 3 centuries. A very strong consistent tradition.