If both partners were Quakers they could be married at a Quaker meeting house, if one of the partners were non Quaker they had to marry in a C of E church. I suggest you study the detail at https://www.qfhs.co.uk/public_html/research.htm#Births and possibly approach the Quaker Family History Society as it also mentions on their helpful site that Quakers had their inhouse burials which would not be on C of E registers