Hi again, Katy,
Sorry I didn't acknowledge your post back in August, but as Christmas is a time when families get together, yesterday was no exception and I picked up the thread of this investigation again with my sister-in-law. The Daniel GATFIELD, blacksmith and churchwarden, who is mentioned in connection with Enclosure awards of 1800 in Hanworth in that link you provided on post 13 is definitely her 4-times great-grandfather, and she is descended through one of his sons, James GATFIELD, b.1807, (also a blacksmith) and then through two generations of namesakes Edward GATFIELD's; the family moved north of the river to Poplar some time after the 1851 Census.
She's actually given me a wonderful photo taken possibly at the turn of the 19thC/20thC showing her great-grandfather in a group of men working on what looks like some kind of railway/tram line, and I'm thinking of posting it on Rootschat so that those very clever people on here can touch it up a little, or at least identify when the photo was taken or where in London it might be situated.
Have you in fact arranged any local history days in Hanworth since you last spoke of the possibility on here...?
Very best wishes, keith