Hi Marble Town
Yes 46 Newton Street Faversham was run by the C of E Diocese (Canterbury).
I will give you a link to follow for information on records from there. Just to let you know formal adoption did not come into force until 1927, so before that it was informal arrangement.
www.baaf.org.uk On their home page, scroll down to bottom of page and you will see 'Adoption search reunion' click on that and it will take you to a new page. On the right hand side of this page look for 'Locate adoption records' click on this and it will open with a search engine. Just type in Faversham and click search and 46 Newton Street will come up, click on that and it will open with information, from that you will see very basic info but if you click on the link Kent County Council (CARDIS) , a very comprehensive listing of records and contacts.
Good luck with your search. Kind regards Jeanette