I have a version of the Hal-an-Tow, from the book which is dubious about the Cutty Wren, so I can't answer for authenticity - especially as neither verse matches the snatch above.

Robin Hood and Little John,
They both are gone to fair, O!
And we will go to the merry green woods
To see what they do there, O!
And for to chase O!
To chase the buck and doe.

With Hal-lan-Tow, Rumble, O!
For we were up as soon as any day, O!
And for to fetch the summer home,
The summer and the May, O!
For summer is a-come O!
And winter is a-gone O!

Where are those bold Spaniards
That make so great a boast O!
Why they shall eat the grey goose feathers,
And we will eat the roast, O!
In every land O!
The land where'er we go.