I wondered when someone would pick up on this. We really don't know yet when "O du lieber Augustin" changed meter and people started stomping out !--- !--, !--, !--,. I don't have the resources to go into the history of the German song.
I don't think it is related to Molly and Polly reels. The texts in the Bodleian Library of "Polly Put the Kettle On" have little to do with the reels either, except for the refrain, which could (probably?) predate the ballads.
Here is another version. The refrain is "shouted":

Lyr. Add: Polly Put The Kettle On, dc

A brother I've a sailor,
The other day came home,
He told us of his travels,
And where he'd been to roam;
He told us of his battles,
What wondrous things he did,
And then he'd hoist his slacks,
And chew another quid.
I gazed with all astonishment,
At his altered style
And judge of my surprise,
Although it made me smile,
For with a voice of thunder,
To my missus shouted out,
"Polly put the kettle on,
We'll all have tea."

Polly put the kettle on, the kettle on, the kettle on,
Polly put the kettle on, we'll all have tea.

No matter wherever I go,
Or when invited out,
As the clock is striking four,
You'ss hear my welcome shout,
Some folks may laugh at me,
For them I do not care.
As I'm a chap as you can see,
I'm jolly everywhere;
So not to break the friendship
I ask you one and all,
Some afternoon when you have time
On me to make a call,
And as the clock is striking four,
It's then I'll shout with glee,
"Polly put the kettle on,
We'll all have tea."

Polly put the kettle on, dc.
(dc. = etc.)

Harding 15, 11(4332). No date. Bobleian Ballads