I am assuming you have contacted Peckham Library where they may have some information, though they may advise that you contact:
The Southwark Local/Family History Group they meet in the Harvard Library, Borough High Street, they too may be able to assist with this research. They do have some very good historians amongst their members.
And they do have their own website.
They have helped me in the past with research of my own.
I used to work in the Post Office in Peckham High Street, and know the outside of the Chapel, which is still visible. And I also visited the Delivery Office and their is a good view of the back of this building from their van park which is above ground level.