Thank you for your reply.
I've only just started investigating this line, and I don't know if there is any connection with the Balscote Adkins. I have noted that there are several wills on Origins.net under Oxfordshire wills.
I had already looked at the Oxfordshire Marriage Bonds, but there are no marriages between an Edward and a Mary or a Rachel.
As Quakers, I assume my Adkins family would have gone to the Banbury meeting, but whether they lived in Banbury or outside I don't know.
I have already made contact with the library at the Society of Friends in Euston Road, and I might need to pay it a visit or go to the Oxfordshire History Centre.
I was wondering if any posters had access to Banbury Meeting data?