Had a lot of hassle finding a unit about 18 months ago. Most of the places we saw that had water were metered, and much larger (and more expensive) than what we neeeded. Give yourself plenty of time to find somewhere if you are going down that route.
There is a place in Bournville on Maryvale road (Pershore Road) that rents units, but out of town will be less expensive.
In Birmingham, you don't have to pay commercial rates on smaller units, and it you find somewhere that operates using a license fee (rather than a long term lease) then you'll have flexibility.
Read the small print as our landlord put it in deep in the contract that rents would increase by 10% every year....