Thank you for your rapid reply. I do know Walthamstow and Forest Gate very well. I was born in Ilford, not far away, and was educated in Wanstead only two miles from Forest Rise in Walthamstow. All these places are now considered as more East London than Essex having been largely swallowed up by the spreading city.
"Handbook to the Environs of London" 1876, by James Thorne is an excellent source book for these regions in Hildebrand's time. The following is a short extract from the entry on Walthamstow: "Walthamstow is sometimes called a town, but the houses collected about the church scarcely form a village, the bulk of the houses being in the outlying hamlets, or streets and ends.." etc. This description is difficult to reconcile with much of the Walthamstow of today.
Forest Rise is to the far south east of central Walthamstow and borders a rare stretch of open heath and forest which has somehow survived in the urban sprawl. The Forest School still exists, a few minutes walk from Forest Rise, and forms probably the largest group of buildings within the open ground.
I wonder if the Walthamstow property was an inherited home where Hildebrand found it more convenient to keep his library and his collections. I do not think there are any 19th century houses still standing in Forest Rise. 26 Bedford Place is now the Beauchamp Hotel.