The other one in his book [an original of which I have] is this. His notes at the end of both songs are of some interest.
The verses with the names in may well have been added for his immediate circle of family and friends. There was a tradition of singing hunting songs in the 'upper hundred' Cheshire families in the 19th c. The "Tarporley Hunt 1833" song - brilliant song! - lists the families who rode with the Cheshire hunt. He would have known them all.

CHESHIRE MAYDAY CAROL

All on this pleasant morning, together come are we,
For the summer springs, so fresh and green and gay
To tell you of a blossom that hangs on every tree.
Drawing near to the merry month of May.

Oh this is pleasant! Singing sweet May-flower is springing
And summer comes, so fresh and green and gay.

Rise up the master of this house, all in his chain of gold,
And turn unto your loving wife, so comely to behold.

Rise up the mistress of this house, with gold upon your breast,
And if your body's sleeping, we hope your soul has rest.

Oh rise up Mister Wilbraham, all joys to you betide. [Mr A.R.]
Your steed stands is ready saddled, a-hunting for to ride.

Your saddle is of silver, your bridle of the gold,
Your bride shall ride beside you, so lovely to behold.

Oh ! rise up Mister Edgerton and take your pen in hand, [Mr D. C.]
For you're a learned scholar, as we do understand.

Oh! rise up Mrs.Stoughton, put on your rich attire, [Mistress E. F.]
You are to have some noble lord or else some wealthy squire.

Oh! rise up the little ones, the flower of all your kin
And blest be the chamber their bodies lie within.

Oh rise up the good housekeeper, all in her gown of silk,
And may she have a husband good, with twenty cows to milk.

And where are all the fair maids that used here to dance,
Oh they have gone abroad from hence, to spend their lives in France..

God bless your house and arbour, your riches and your store.
We hope the Lord will prosper you, both now and ever more.

So now we're going to leave you, in peace and plenty here,
We shall not sing this song again, until another year.

Pp 239 & 240, "Ballads & Legends of Cheshire", Egerton Leigh, August 1866. [copied by him from Palatine Anthology : a collection of ancient poems and ballads, relating to Lancashire and Cheshire, by Halliwell-Phillipps, J. O. (James Orchard), 1820-1889 [Published 1850.]