Viv
It would have been a circulating library for which people paid to borrow books. I can remember them in boot and WH Smiths in the 1950s. They were often associated with booksellers or similar. This is almost certainly associated with a stationers (which is similar). The 1904 Kellys lists no 252 High st Erdington (see name when looking closely at photo), as John Barrett ,grocer, near the end of the street and 6 shops away from the Baptist chapel (which would be on the far right.) No 246 is Alfred Rodway, Tailor (Rodway in photo) and two doors up from there (where Library sign is) is no 242.John Dodd , tobaconist & stationer