There is a Quaker burial ground at Sibford Gower, about 5 miles from Banbury. It is opposite and down the hill from a wonderful Cotswold pub called the Wykham Arms (the map on the pub website will help you find it:
www.wykhamarms.co.uk/).
If you are still searching for info, I've probably got a contact number for one of the Friends who manages the burial ground, and might have a list of burials, but I don't want to post it publicly. I'm new to this site - is there a way to communicate 'offline'?
There is also a Quaker Boarding school at Sibford Ferris, the next village, where you might be able to find more information.
Dee