Lyn
If you look elsewhere, on a thread with a name very similar to this you will see that Dennis Williams pinpoints Button Alley. He says that Showells Dictionary of Birmingham says it was the forerunner of Masshouse Lane. Though on a map he saw it was marked as an alley running between Masshouse Lane and Chapel Street.
He didn't post an image of the map and he didn't give it a name or date, I will ask him about it next time I speak to him. In the meantime this map shows the alley in question running in between the two names streets (I think).