Dormant now for another 7 years.
I returned to this for Queen Elizabeth's Jubilee.
The tune as noted by MMario above is similar to that in the Scottish Student Songbook, as noted above. But with slight variations to words & music (different key, different positioning of syncopation,) I won't claim the kudos for typing this up. I just copy/pasted Mmario's into Folkinfo and got it automatically transposed, & then I went through adjusting!

X:1
T:Here's a health unto his Majesty
C:from ~1670
M:C
L:1/8
K:Amaj
A B|c2c2c2c2|B2c2A2A B|c2c2c2B A|B4A2(A B)| c2c2c2c2|B2c2 A2A B|c2c2c2B A|B4A2c2|c3d e2c2| f2f2e2c2|c3d e2c2|B3AG2(A B)|c2c2c2c2|B2c2!fermata!E2A B| c2c2c2B A|B A B c d2A B|c2c2c2B A|B4!fermata!A2||
w:Here's a health un-to his Ma-jes-ty, With a fa la la la la la la! Con-*fu-sion to his en-e-mies, With a fa la la la la la la! And he that will not drink his health, I wish him nei-ther wit nor wealth, Nor_ yet a rope to hang him-self, with a fa la la la la la la la la la with a fa la la la la la la