I've managed to find a map of sorts showing the location of Bingley Hall between Edwards Place and Alfred Place which I think is the street shown in the previous photo. It looks as though Bingley Hall was shielded from Broad Street by the Prince of Wales theatre which is probably why I don't remember it from my frequent visits to Gas Street basin. Interestingly, this theatre appears to have taken a direct hit during one of the first bombing raids on Birmingham on 9 April 1941 and was never rebuilt until finally demolished in 1987.