Thank you, everyone, for that. Great information.
Not that it is likely to fascinate anyone very much.... but I will explain my interest in this important building (of which there seems to have survived little information, at least online).
First, it was the digs of Home Guard men from all over the country who were attending courses at the Street Fighting School in Bristol Street, 1942-1944. (Sorry, yawn, yawn!)
Second, my great-uncle had some, perhaps even significant, involvement with it. Maurice Jacob Myers (1874-1933) was educated at King Edward's School, then in New Street of course, from around 1885 to 1890 and later trained elsewhere as a "Typewriter", (typist/stenographer). Some time after April 1891 he emigrated to New York and earned his living there as a Stenographer. This somewhat exotic change of location perhaps mirrored the adventurous spirit of his own father who had set off from Birmingham to California as a nineteen-year-old in about 1851, in order perhaps to cash in, a little late, on the Gold Rush, and returned in 1859. Later in New York Maurice suffered total blindness, said to be the result of a firearms accident. Returning to Birmingham, he obtained assistance from the Blind Institute and became a noted Braille shorthand and typewriter operator. On one occasion he took dictation from the Prince of Wales (the future King Edward VII) during an exhibition in London. In 1918 he joined Midland Societies for the Blind as an organiser and canvasser. In 1933, he was being driven by friends on a fishing trip to Worcestershire, when the car in which he was travelling was in collision with another. He was taken to the Cottage Hospital in Halesowen where he died from his injuries.
My Great-Uncle Maurice, whom I never met....
Chris