I am not sure if this helps but in 1881 census Henry Toye was director of the Home for the Fatherless Orphanage. His children were the teachers and matron, living in the orphanage. In 1881 its address is George Terrace, Lewisham Road. By 1891 it was just for girls. At the time of the 1901 census, itts location was identified as 64 to 72 Lewisham Road, Greenwich and it was run first by Henry Toye, then by a son of the same name (1901 census).
I found a request for information on Curious Fox which states in part "In 1871 census my Ggrandmother Amelia Hutchins aged 8 years (orphan)poplar although her mother was still alive. was in a girls orphanage George Terrace Lewisham Greenwich. Run by a Henry Toye,s Lewisham FHS and the Metroplitan archives have no information about this place".
This would make it seem that the institution was opened before 1871. In that census, several of Henry's children were teachers but his occupation was listed as "Fancy Repository". The reference to the Hutchins mother and the orphanage name leaves the impression that this was a home for destitute children more than for the parentless. It may also have had an association with King Edward Certified Industrial Girls School Andrews Rd Northeast, Hackney, London. They show up sequentially in an 1896 survey.
I would appreciate it if anyone could give me more precise information on this orphanage.