Just for info Poplar Cottage is still there today, much enlarged. It's had various additions over time according to Bill Dargue's site and part dates back to late 18th century. Viv.
https://billdargue.jimdo.com/placenames-gazetteer-a-to-y/places-m/moor-end-green-erdington/
https://billdargue.jimdo.com/placenames-gazetteer-a-to-y/places-m/moor-end-green-erdington/