Just came across this excellent site,
http://www.anderston.ukpals.com/home.htm
Which I can heartily recommend.
It states the the building was the former St. Peter's Church, and it remained open at No.'s68-72 oswald Sreet till the late 1950's. the ground floor held an aquarium and the rest of the beasties were up the stairs.
By the looks of the pics on the site, there were two cghurch's right close together, and both had the double stairs at the front.