This photo of John's Hill gives some idea of what Breezer's Hill, a little to the west, might have looked like when MJK was resident.
Imagine a fairly new wool warehouse taking up the whole of the western (right) side of the street, a pub (the White Bear) at the NE corner, and a former pub (the Old Red Lion) on the SE corner (79, Pennington Street). In between were just 4 small houses.
It seems most likely that MJK was at 79, Pennington Street, but nos 1, 2 and 3 Breezers Hill were also apparently brothels at one time or another.
The buildings in the background are part of the London Dock.