A search here and elsewhere on the net finds several songs with the same, or similar titles. At least one with the same chorus lines, but I can't find this precise one, so I'm adding it here. Melody is also provided in ABC format
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HEAVE AWAY, MY JOHNNY
Collected and arranged by Cecil J Sharp

(Chanty.)
1. As I walked out one fine morning all in the month of May,
(Chorus.)
Heave away, my Johnny, Heave away.
(Chanty.)
I overtook a fair pretty maid, And unto her did say.
(Chorus.)
Heave away, my jolly boys, We're all bound away.
(Chanty.)
2. O where are you going to, my pretty maid? I unto her did say.
(Chorus.)
Heave away, my Johnny, Heave away.
(Chanty.)
I'm going a milking, sir, she said, All in the month of May.
(Chorus.)
Heave away, my jolly boys, We're all bound away.

(Chanty.)
3. Shall I go with you, my fair pretty maid? I unto her did say.
(Chorus.) all chorus parts as for verses 1&2
(Chanty.)
O yes, if you please, kind sir, she said, All in the month of May.
4. O what is your father, my pretty maid? I unto her did say.
My father's a farmer, kind sir, she said, All in the month of May.

5. O what is your fortune, my fair pretty maid, I unto her did say.
My face is my fortune, sir, she said, All in the month of May.
6. Then I cannot marry you, my pretty maid. I unto her did say.
Nobody asked you, sir, she said. All in the month of May.

X: 1
T: Heave away my Johnny
M: 6/8
L: 1/8
Z: NP 06/09/2017
K: A
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w: 1.As I walked out one fine mor-ning all in the month_ of May, Heave a-way,__ my John-ny, Heave_ a-way.____ I ov-er-took a fair pret-ty maid, And un-to her_ did say. Heave a-way,__ my jol-ly boys, We're all bound_ a-way. 2.O where are you go-ing to, my pret-ty maid? I un-to her_ did say. Heave a-way,__ my John-ny, Heave_ a-way.____ I'm go-ing a milk-ing, sir,_ she said, All in the month_ of May. Heave a-way,__ my jol-ly boys, We're all bound_ a-way. 3.Shall

From: A Selection of Collected Folk Songs arranged by Cecil J Sharp and R Vaughan Williams
Published by Novello & Co (Undated)
Copyright (shown separately for this song) Novello & Co 1909
NP