I found many variants of this song on the Internet. I can't tell for sure which is the original copyrighted version, so I listed my best guess first and listed the variations below.

KNEES UP, MOTHER BROWN
(E Harris Weston, Bert Lee. Copyright EMI, 1938)

1. Knees up, Mother Brown! Knees up, Mother Brown!
2. Under the table you must go.
3. Ee-i-ee-i-ee-i-oh!
4. If I catch you bending, I'll saw your legs right off.
5. Knees up! Knees up!
6. Don't get the breeze up!
7. Knees up, Mother Brown!

Oh, my! What a rotten song! What a rotten song! What a rotten song!
Oh, my! What a rotten song! What a rotten singer, too!

Ow's yer farver? All right!

[VARIANTS FOR LINE 2:
2a. This ain't the Lambeth Walk, you know.
2b. Come along, dearie, don't be slow.
2c. Come along, dearie, let it go.
VARIANTS FOR LINE 4:
4a. And if your bones are creakin', don't let it get you down.
4b. It's your blooming birthday, so wipe away the frown.
4c. It's your blooming birthday. Let's wake up all the town.
VARIANTS FOR LINE 6:
6a. Never let the breeze up!
6b. Never get a breeze up!

[There are kids' versions, recorded by Raffi and others, that contain the following additional verses. (There may be more.)]

Prancing up and down, prancing up and down,
Prancing, prancing, never dancing,
Prancing up and down.

Whirling round and round, whirling round and round
Whirling, whirling, ever twirling
Whirling round and round

Hopping on one foot, hopping on one foot,
Hopping, hopping, never stopping,
Hopping on one foot.