Nice post - I take it these are the Cottage Homes that were off Orphanage Road ?
They don't look like the ones off Fentham / Highcroft Roads.
If at first you don't succeed, try again, then give up - no use being a fool about it !
There were two homes, one in Fentham road, which ajoined Highcroft hospital, that was the one my wife was in, for exactly the reason you say, her parents had problems.
The other was in Orpanage road Erdington, the exact location I don't know.
The Cottege Homes on Orphanage Rd were on the Left going from Chester Rd towards Erdington just before you got to Holly Lane. Last time I went down there the gate posts were still there. It is now a little road that leads down to some warden controlled bungalos for old folk.
Highcroft Hospital and Cottage homes 1928
Acknowledgment to www.britainfromabove.org.uk
The cottage homes I knew about were by Highcroft hospital, I didn't know anybody who was there, but I think my eldest sister went to school at wood end lane ? And one I'd her friends lived there.,, I am found back a few years