Later census records for Robert, Rebecca & Alexander only give Ireland as place of birth.
I do not know if any formalities/documentation were required upon entry to England or the Isle of Man, or if they would include town or county of birth.
Unfortunately, as there were Nugents in Ireland since the 12th century, they are all over the Island.

There is a Nugent forum that you may want to check:
genforum.genealogy.com/nugent/all.html