I was actually in Bedford library yesterday looking up my own stuff, I took a look for your dude but was unable to find a thing. I asked about poor relief records, and according to the librarian it would be pretty near impossible to find - even if you found the right parish, and the right year, then the child would more than likely be listed only by christian name or apparently might be given the surname of the place they were given a free apprenticeship (or take the masters) ... this is where the librarians own name came from when a over a number of years a barrel maker sent food for, and finally took in + apprenticed her great grandfather or great great grandfather...he was given the surname Cooper because of it.
All very interesting stuff but I'm afraid it doesn't help you very much. Sorry!
I'm going back at some point next week, if there's any other info that could help you?