Alice Gomme, 1898, "The Traditional Games of England, Scotland and Ireland," Vol. 2, pp. 25-35, gives two tunes for the rhymes, as well as an 'older' version of the last five bars, ans sixteen versions.

A version from Northhamptonshire:

XVI.
PANCAKES AND FRITTERS

Pancakes and fritters
Says the bells of St. Peter's;
Where must we fry 'em?
Says the bells of Cold Higham;
In yonder land thurrow (furrow),
Says the bells of Wellingborough;
You owe me a shilling,
Says the bells of Great Billing;
When will you pay me?
Says the bells of Widdleton Cheney;
When I am able,
Say the bells at Dunstable;
That will never be,
Says the bells of Coventry;
Oh, yes it will,
Says Northhampton Great Bell;
White bread and sop,
Says the bells at Kingsthorp;
Trundle a lantern,
Says the bells at Northhampton.

from Baker, "Words and Phrases".

Gomme comments: "The procession of a criminal to execution was generally accompanied by the tolling of bells, and by torches. It is not unlikely that the monotonous chant of the last lines, 'Here comes a light to light you to bed, &c., indicates this.""

Leeneia, to children, the "chop'n bill to chop of the last man's head, Chop--chop--chop--chop" is the 'topper' of the game.
Shame on you for that pillow- sweet head nonsense!
May children continue with the execution, as they have for the last two centuries!