The information on the Crozier family that I have is from two sources:
1. The informal letter of adoption for my mother-in-law is signed by May Crozier, The Grange, 53 Wake Green Road, Moseley and dated 22 October 1925. Even with my healthily cynical genealogist head on, I can think of no reason why any of this would be a lie.
2. There is then the information in the Birmingham Family History group thread. I do not have access to electoral rolls and local Birmingham documents, so just trust the people who have responded.
The one lack of clarity appears to be over who was actually resident at 53 Wake Green Road Moseley on electoral rolls in the 1920s, especially 1925 and 1926.