Further to my post at 1806:
A bit more research suggests that the schools on the corner of Gerrard Street and Lozells Street were Lozells Girls School (on the right, as you turned right when walking away from Wheeler Street) and "the infant and junior schools" (with no name given in the relevant post, on the left if you turned left off Gerrard Street).
Perhaps that's what Bazile is referring to? If so, it seems to have been Lozells Street Primary School:
http://birminghamhistory.co.uk/forum/index.php?threads/lozells-st-primary-school.32237/
It was originally called Lozells Street Board school, having been set up in 1882. Further, it seems that there was actually an entrance to the school on Gerrard Street, which would satisfy Bazile's description.
Pictures here:
http://www.birminghamforum.co.uk/index.php?topic=2292.374