Rooms in University halls of residence are primarily reserved for first year students and international students. However rooms may become available throughout the year, check with BCU's Accommodation Team on 0121 331 5191. Also, have a look at the BCUSU's facebook group for any rooms which are being advertised.
There are also a number of private halls in Birmingham, not partnered with BCU. Rents tend to be more expensive, but often include bills such as free internet access and energy supply. This site provides really useful list of the halls in Birmingham along with ratings.