The Birmingham Coffee House co (The Cobden) seems to be part of the Cobden Hotel, which was on the corner of cheryy St. It would be where the southern tip of Rackhams (sorry House of F!!) is now . As to the other earlier photo, in 1888 the only Jeromes listed in Kellys are a botton manufacyurer in Gt Hampton st and a dressmaker in Bradfor St, so that's not much help in determining where it is
Mike
Mike