The May-day garland in The Oxford book of Carols (no. 48)has some similar verses to The May-day carol and May-day carol 2 in the DT.
The tune is the same as Steeleye span used for The spotted cow - CHR 1008.

MAY-DAY GARLAND

Traditional
The Oxford Book of Carols No. 48

I've brought you here a bunch of may!
Before your door it stands:
It's well set out and well spread about,
By the work of our Lord's hands:
It's well set out and well spread about,
By the work of our Lord's hands.

This morning is the first of May,
The primest of the year:
So ladies all, both great and small,
I wish you a joyful cheer:
So ladies all, both great and small,
I wish you a joyful cheer.

Then take your bible in your hand,
And read the scriptures through:
And when the day of judgement comes,
The Lord will remember you:
And when the day of judgement comes,
The Lord will remember you.

The clock's struck one! I must be gone!
No longer can I stay.
If I should live to carry again,
I'll call another May:
If I should live to carry again,
I'll call another May.