JM Carpenter's Collection has many instances of the song in recorded and or written format. Many different informants. These range from Edward Robinson, you might have learned it any time between 1846 and 1877, to George Simpson, who probably learned it around 1888 and 1889.

I find 7 samples in the collection, which were noted or recorded 1927-1929.

1. BOYLE, GEORGE

>LEAVE HER JOHNNY

Text file. Includes line:
"Leave her down in London town"


2. KING, STANTON

>LEAVE HER, JOHNNY, LEAVE HER [LEAVE HER JOHNNY]

Text, incl.: "Oh the times are hard and the wages low"

3. MIDDLETON, JOHN

LEAVE HER, JOHNNIE, LEAVE HER

Text: "O the times are hard and the wages low"
A recording also exists.

4. MURRAY, JACK

>LEAVE HER, JOHNNY,
Rec., containing 2 verses. Has the first verse.
"Oh the times are bad and the wages low". Second verse may start, "The grub was bad...."

5. PAGE, CAPTAIN MARK

Apparently there's a recording of the song. No further info.

6. ROBINSON,EDWARD

>LEAVE HER, JOHNNY

Text: "We'll pump her out and go on shore".
There's a recording, too.

7. SIMPSON, GEORGE

There's a recording.