This is the former Midlands Bank Limited bank on the corner of Bennetts Hill and Waterloo Street. When HSBC took over the Midlands Bank, they eventually closed this old branch. It was built / opened in or after 1834.
It was designed by the architect Thomas Rickman. It is his only surviving building in central Birmingham. His style was gothic. It is Grade II listed. Address is 26 - 33 Bennett's Hill.
I'm not sure, but I think the building is currently vacant / empty - not in use. No 33 Bennett's Hill is occupied by Webb Gray & Partners Ltd, an architecural practice.