The song seems only to have been noted from a few Traveller (Gypsy) women, and in the second half of the 20th century.  Here is another:

HOPPING DOWN IN KENT

(Mary Ann Haynes, Sussex, 1974. Noted by Mike Yates)

Now hopping's just beginning,
We've got our time to spend.
We've only come down hopping,
To earn a quid if we can.
With the tee-i-ay, tee-i-ay, tee-i-ee-i-ay.

Now early Monday morning,
The measurer he'll come round.
"Pick your hops all ready,
And you'll pick them off the ground".
With the tee-i-ay, tee-i-ay, tee-i-ee-i-ay.

Now early Tuesday morning,
The bookie he'll come round;
With a bag of money,
He'll flop it on the ground.
Saying, "Do you want some money?"
"Yes sir, if you please,
To buy a hock of bacon
And a roll of mouldy cheese".
With the tee-i-ay, tee-i-ay, tee-i-ee-i-ay.

They say all hopping's lousy,
I believe it's true.
Since I've been down hopping,
I've got a chat or two.
With the tee-i-ay, tee-i-ay, tee-i-ee-i-ay.

Early Saturday morning,
It is our washing day.
We boil 'em in our hopping pot,
And we hangs 'em o'er the ground.
With the tee-i-ay, tee-i-ay, tee-i-ee-i-ay.

Hopping is all over,
The money is all spent.
I wish to God I'd never done
No hopping down in Kent.
With the tee-i-ay, tee-i-ay, tee-i-ee-i-ay.

I say one, I say two,
No more hopping shall I do.
The tee-i-ay, tee-i-ay, tee-i-e-i-ay.

This appeared, together with Louise Fuller's set as quoted by Mick above, in Mike Yates' article English Gypsy Songs (Folk Music Journal vol.3 no.1, 1975).  The tune, as she sang it, contained a number of variations; the midis listed below are for verses 1, 3 and 7.  They will make their way in time to the  Mudcat Midi Pages:  meanwhile they can be heard via the  South Riding Folk Network  site:

Hopping Down in Kent (verse 1)
Hopping Down in Kent (verse 3)
Hopping Down in Kent (verse 7)

I have omitted a couple of grace notes, and, in verse 3, combined a couple of notes and split another to accomodate the lyric.  There were also variations in verses 4 and 5.  Incidentally, the performance of Hopping Down in Kent on Topic's  Voice of the People Volume 5: Come All My Lads That Follow The Plough,  though credited to Mary Ann Haynes, is actually by Louise Fuller; there was a mix-up when the masters were being prepared.

The text Roger quotes above looks to be from the Albion Dance Band; they recorded an arrangement of the Haynes version, collated with parts of the Fuller one, though the sleevenotes (The Prospect Before Us, Harvest/EMI 1977) weren't that specific.  I should imagine they got the material from the FMJ.