I note in the introduction the author refers to this, and says of it "Walsingham ...is almost certainly built up on a traditional foundation."

Which seems likely enough, in the light of his pretty ferocious celebration of gruesome public mass executions of Catholics, as shown in a couple of the ballads in the Miscellaneous Ballads section.

I see there is another referance to Walsingham in The Garland of Goodwill, in a Dialogue between Truth and Ignorance.(Ignorance being a Papist of course):

Ignorance

But our Lady of Walsingham was zure an holy Zaint:
And many men in pilgrimage,
did shew to her complaint.
Yea zweet Zaint Thomas Becket,
and many others moe:
The Holy Maid of Kent, likwise
did many wonders zhow,

Truth.

Such Saints are well agreeing,
to your profession sure:
And to the men that made them
so precious and so pure.
The one was found a Traitor,
and iudged worthy death,
The other eke for Treason
did end his hatefull breath.