Edith Fowke collected a Canadian version entitled The Faggot Cutter from Mrs Gordon Clarke.
Here it is from her 'Traditional Singers and Songs From Ontario'.
It bears striking similarities to a song collected by George Gardiner in Hampshire called The Roving Bachelor which was published in one of Frank Purslow's selections from the Hammond and Gardiner manuscripts..
Jim Carroll

THE FAGGOT CUTTER

1.        Oh, here's to the faggot cutter; he works at home with me.
He'll start to work at six o'clock; he quits whene'er he please.
He cuts his wood in faggot bundles, he lays it on the ground,
Then he takes his cord and binds it. Drink round, my boys, drink round.

Chorus: Drink round, my boys, drink round, my boys,
Until it comes to me,
For the longer that you sit and drink,
The merrier you will be.

2.        For I owe no debts, I pay no frets, no troubles do I find.
I have no cradles for to rock, no babies for to mind.
I'm bound to live a single life no matter where I roam;
Then no man in life will court my wife when I am far from home.

3.        For if I should marry a good-looking girl, a couple we'd surely be;
If I should marry a homely one, the boys would laugh at me;
If I should marry a big one, she would surely knock me down,
And small woman are darn contrary. Drink round, my boys, drink round.

45. THE FAGGOT CUTTER. This lively old English drinking song was apparently sung at harvest-home suppers, for it follows the pattern of other harvest healths of which the most common was "Here's a Health To Our Master." In 1893 Lucy Broadwood gave this description of the ritual: "At the harvest suppers up to some twenty years ago, while the guests were still seated at the table, a labourer carrying a jug or can of beer or cider filled a horn for every two nfe'n, one on each side of the table; as they drank, this old harvest song was sung, and the chorus repeated, until the man with the beer had reached the end of the long table, involving sometimes thirty repetitions of the first verse. After this the second verse was sung in the same manner."
The only song resembling "The Faggot Cutter" that I have located is "The Woodcutter," published by Miss Broadwood's father in 1843 and reprinted in 1890. Its first stanza and refrain correspond fairly closely to Mrs. Clark's, but its second stanza is the common "Here's a health unto our master." A "Suffolk Harvest Home" noted by J. H. Bell in 1846 also has a refrain very close to that of "The Faggot Cutter" although his stanzas follow the common form.
"The Faggot Cutter" probably dates from the eighteenth century when country men went into the woods to cut branches and bind them into bundles known as faggots which were sold for fuel. Before the Industrial Revolution the faggot cutter was a familiar figure in Britain. The refrain may have been added at a later date for a version sung by ninety-one-year-old Michael Leahy of Warsaw, Ontario, did not have any. He called it "I Mean to Lead a Single Life," and his second and third stanzas paralleled those of Mrs. Clark, but his first and last stanzas were different.
Mrs. Clark says that her Granddad LeBarre used to sing this as he dandled her on his knee. It was also a favorite of her father, who would sing it to tease her mother.

References:
Broadwood: Sussex Songs, 30-31.   Broadwood, 150-1.   Dixon, 190-1. Record: Topic 12T140 (Mrs. Clark) .