I was in Summer Lane yesterday and took these photos.
Afraid the building is in sorry condition, would love to go in and up to the top, but apparently extensive work and money are needed to stablise and maintain the building.
The sign looks like the main structure of the 'A' has gone at some point.The top is filled with some sort of growth,but couldn't see any evidence of pigeons.
Excuse quality of first two photos, large magnification used.
Also reminds me of the flatiron building in New York.
One you allow vegetation to start growing on your building it can sound the death knell of the building, it gets between the courses and forces the brickwork apart. Sometimes on buildings with climbing ivy it is only the ivy holding it together because the ivy root (tentacles) has pushed all the mortar out.
A little info here for Model Lodging House - perhaps a workhouse
https://www.workhouses.org.uk/Birmingham/