Mad got some info for you!
It is indeed Wrens nest farm!
it did exist
it aint the Priory farm one
So I am in possesion of an ordanace survey copy from the archives for 1919
it clearly names and shows the farm and the Priory one to the left
on the later ord map in 1938 it is still there .
Now Dudley Archives have some Dudley Estate archived recoreds
the info in there could well house your Wrens nest info ...then again might not....
the info covers leases, Wills, surveys and bks refs- this gives info on who owned the land, who rented, what land was used for etc.
You would have to either pay someone to go thru it, or get Dudley to go thru it using their research service.
If you give me your email I will send you a scan of this ord map section
if anyone else wishes a copy pm me
