The unnamed "old Sussex singer" was Henry Hills of Lodsworth in Sussex, and this song was noted from him by W. P. Merrick in January, 1900. Frankie Armstrong seems to have altered his text somewhat (and reversed the sexes of the participants), so, on the basis that it's always best to go back to a traditional source where we can, here it is as he sang it:

LOW DOWN IN THE BROOM

(Noted by W.P. Merrick from Henry Hills of Lodsworth, Sussex, in 1900)

'Twas on last Monday's morning, the day appointed was
To walk out into a meadow-green field to meet a bonny lass.
To meet a bonny lassie, to bear her company,
For she's low down, she's in the broom, a-waiting there for me.

I look'd over my left shoulder, to see whom I could see,
There I spied my own true love, come tripping down to me;
Her heart being brisk and bonny, to bear me company,
For she's low down, she's in the broom, she's a-waiting there for me.

I took hold of her lily-white hand, and merrily was her heart,
"And now we're met together, I hope we ne'er shall part."
"Oh part, my dear? no never, until the day we die."
For she's low down, she's in the broom, she's a-waiting there for me.

From The Journal of the Folk Song Society, vol.I, issue 3, 1901.

Ms. Armstrong's line How sweet and pleasant was the day I kept [him] company seems to have been introduced from another set of the song printed in Frank Purslow's The Wanton Seed (EFDS Publications, 1968) which had a longer text collated from two traditional examples from Hampshire, and a broadside.

Since a song is of limited use without its tune, I've made a midi from the notation in JFSS. Until it appears at Mudcat Midis, it can be heard via the South Riding Folk Network site:

Low Down in the Broom (midi)

There are two examples of a broadside issue by an unknown printer at Bodleian Library Broadside Ballads, the clearer of the two being:

Whitsun Monday. A new song ("It was on Whitsun-Monday ...")

There is also a Scottish Low Down in the Broom, beginning My daddy is a canker't carle, which is a relative (textually) of the English versions; the sexes of the participants there follow Ms. Armstrong's arrangement. Opinions differ as to which is the older; Frank Kidson thought the English song to be the "original", while Frank Purslow considered the reverse to be more likely. Of the Scottish version, the Bodleian has two issues by Catnach of Seven Dials on large songsheets, and the following:

Low down in the broom ("My daddy is a canker'd carle ...") -printer and date unknown.