Sorry Nick. But it was Fred Holman, not the singer Harry Holman, who composed the song. This is my note to the song from a Musical Traditions CD:

Better known as Shooting Goshen's Cock-Ups, the incident happened on the Goshen Estate near New Addington in Surrey, and the song was composed by Fred Holman, of Tatsfield in Surrey; who also wrote the song Patsy Flanaghan (Roud 16632), both of which Pop Maynard used to sing (Musical Traditions MTCD309-10). The tune comes from an earlier song, Bow, Wow, Wow or The Barking Barber, which was popular in the 1780s. It was sufficiently well-known to be parodied in Alice in Wonderland.

Fred Holman would write out the words for the price of a pint - so, obviously, the song developed over time. Here's a 'complete' version of his text:

Oh if you'll listen for a while, a story I will tell you,
And if you don't attention pay, I'm sure I can't compel you,
But since you've asked me for to sing I'd better start at once
And tell you how I got six weeks and my mate got two months.

Chorus:
With me row dow, dow, dow,
Fol de riddle oddy,
With me row dow, dow.

It happened on one Monday night; myself, two more, and Clarky,
Went out a-pheasant shooting in a place we knew was narky;*
Three keepers rushed upon the spot when the guns began to rattle,
And my two mates they done a bunk and left us to the battle.

We tried our best to get away, but vain was our endeavour,
We should not have been taken if we had all stuck together,
But me and Clark was captured and taken to the lock-up,
And charged before the magistrate for shooting Goshen's cocks up.*

At ten o'clock next morning to the Town Hall we was taken;
We thought our case could settled be, but we was quite mistaken;
We was put back upon remand 'til the fourteenth of November,
And if you read the Croydon Times, I'm sure you will remember.

When our remand was at an end, for Croydon we came steering,
And soon before the magistrate we stood to have our hearing;
Our case it was so very clear, it did not want much trying,
When our time it was knocked down to us, our wives they started crying.

Now we asked them to propose a fine, but that they would not sanction,
Then soon we knew our residence would be in a public mansion;
The magistrates to me I'll own, they acted like a neighbour,
They let me off with six weeks, but give Clark two months' hard labour.

At four o'clock that afternoon for Wandsworth Jail we started,
Our friends were there to see us off, they all seemed broken-hearted;
Whilst rattling up to Wandsworth Jail our minds seemed to bewildering
About our future station and our wives and little children.

At Holloway our clothes were searched and everything was taken
Away from us, the warders thought, but they were quite mistaken,
For as I paced my lonely cell, I couldn't help but smile,
To think I had deceived 'em; I'd got baccy all the while.

Now the first four weeks I was in jail they put me grinding flour,
Likewise a-pumping water, boys, into a lofty tower;
My strength it quickly did decrease; I thought it rather cruel,
To make a man work hard all day on brown bread water gruel.

Now the twenty-fourth of December, my time it did expire;
When I got out I had some scran, that's what I did require,
And when I'd had a drink of beer, I really felt quite merry,
To think my mate he don't come out 'til the middle of January!

* narky - having narks (keepers) there.
* cocks up - almost always sung as cock-ups.