Saw your message and wondered if this is of any use to you:
I have a family of Mulleys in my ancestry that originally hail from Suffolk. They moved north to the Bishop Aukland area (between 1872 and 1876). There were several children to the family, my GGgrandfather moving to Leeds in the early 1890's which is where I was born. However I do not know if the other siblings stayed in Co Durham area or moved away.
There seem to be numerous Mulleys from the Suffolk area. Although the name does sound Irish, from what I have read from other people, it most probably isn't.
I found another Mulley message board on: http://genforum.genealogy.com/surnames/
one person had several explainations of the origin of the surname.
please let me know if you want more information on my Mulley line, I would like to know more on your South Shield connection if you have the information.