I know this is almost 10 years old and I don't know if anyone is still looking at this, but just in case...
First, I think you are mistaken about Elizabeth Warrington's birth date. I believe she was born in 1735, not 1765. She and John had a child John in 1765/6. Taking it further back, John's (1709) parents were John (1675-1747) and Elizabeth Roe. John's (1675) parents were William (1641-1700) and Joan Battle (1641-1717). William's father was another John Peberdy (1616-1660). That is as far as I have been able to go. If you (or anyone else) has any more on this, I'd love to hear it. Thanks