Hi Atlanta,
Hope this may be of help as I was searching an adoption last year.
Go to
www.baaf.org.uk (British adoption and fostering) site. On home page on the right under red banner click on Adoption Search Reunion, this will take you to another link, on left hand side click on search for location of adoption records. On key words for search enter hackney, scroll down results and to the bottom you will see St Margaret's Nursing home, the address as you gave. There doesn't seem to be much info on records but does give organisation names that may help. Click on St Margaret's and it will show you who may be involved with adoptions, click on each individual organisation name and that will give you contact details.
I myself had 4 organisations to contact, all of whom were very helpful and I actually found out the adopted persons file is at London Metropolitan Archives archived under Middlesex County Council. We have registered on the contact register and this year we are going for a search and contact. We do have o use a intermediary service.
Good luck with your search
