As JMW Turner's father, William, was given as being from South Molton, Devon would suggest contacting the local museum.
http://www.southmoltonmuseum.org/

These websites may also help.
http://www.tate.org.uk/art/research-publications/jmw-turner/...

http://www.heardfamilyhistory.org.uk/ghtout/p185.html#head3
(mentions the Turners in the Colebrooke, Crediton area)
http://genuki.cs.ncl.ac.uk/DEV/Colebrooke/ (inc OPC)

http://genuki.cs.ncl.ac.uk/DEV/SouthMolton/SouthMolton1850.h...
gives several Manning entries.

http://www.achurchnearyou.com/ashill-st-stephen/ (Uffculme)
http://genuki.cs.ncl.ac.uk/DEV/Uffculme/ (inc OPC link)
(Uffculme to Colebrooke approx 25 miles). Hope it helps.