I struggled a bit to relate your description to my location, Bazile. Perhaps a map would be easier?
Unfortunately Gerrard Street lies right on the edges of two 25" OS sheets but, having looked at the both, I can assure you that there's no school shown on the northern of the two sheets. The top edge of the southern sheet is shown in my illustration here:
http://upl.co/uploads/GerrardStreet11524679009.jpg
The school facing the mission hall, across Lozells Street, would seem to be Lozells Girls School. The 'schools' (note the use of the plural, presumably for 'infant and junior') diagonally across from the mission hall appear to be Lozells Street Infant and Junior Schools.
As my previous post shows, although the front of the building was on Lozells Street, there was also an entrance on Gerrard Street.