I think this is the song that you mean

May Song (As sung by Mum Johnstone)


Good morning lords and ladies it is the first of May,
We hope you'll view our garland it is so bright and gay,
For it is the first of May, oh it is the first of May,
Remember lords and ladies it is the first of May.

We gathered them this morning all in the early dew,
And now we bring their beauty and fragrance all for you,
For it is the first of May, oh it is the first of May,
Remember lords and ladies it is the first of May.

The cuckoo comes in April, it sings its song in May,
In June it changes tune, in July it flies away,
For it is the first of May, oh it is the first of May,
Remember lords and ladies it is the first of May.

And now you've seen our garland we must be on our way,
So remember lords and ladies it is the first of May,
For it is the first of May, oh it is the first of May,
Remember lords and ladies it is the first of May.


Source: Fred Hamer: Garners Gay (EDFS Publications 1967)


Fred Hamer comments:
This carol Mrs. Johnstone learned from her grandmother who came from Carlton, and it seems to have been used in some villages near the Northamptonshire border. This is the fullest version I have come across so far.