Hi,
Re Rainsfords just replied to a request from someone at Rootschat, never heard of this site before!
I am related to the Rainsfords, Thomas was my great grandfather and Florence was his wife (nee Wilks). I have a photocopy of Thomas' birth certificate which has been handed down the family to me and on that it states that Thomas Wilks was born on 16th April 1874 at Leopold Street Aston to Edward Rainsford and Sarah Rainsford formerly Lapwell. The birth was registered on 6th May, 1874 Sub district Deritend Warwick where Sarah had made her mark.
If you have access to Ancestry then I had download the certificate to my tree - Hardeman/Doody/Harris where you will also find photos of Sarah and Edward and also one of Thomas and Florence.
I have looked at your discovery and will now need to do more research myself.
I would love to hear more of your search and if I can be of any help please let me know.
Good luck