There's nothing in Brum that I'd recommend, I'm afraid. The nearest club to you that I can think of is the Nottingham Uni club:
If you're interested to see some shiai, it just happens that there's a little tournament in Sheffield next weekend that should be interesting.
The annual student national event has gone international this year; there's a team coming over from Waseda University, accompanied by Shishida Shihan. Drop me a mail if you'd like more details.