I live just over an hour away from Birmingham and have relatives who live there so am in the area quite often.
Sadly I can't recommend any bars with gluten-free beer though. Only thing I could suggest would be to ask in a bar that has "guest ales" sometimes to see if they'd get one in to try in case it proved popular. You never know, it might bring in coeliacs from all over the place to drink their beer if they advertised it well.
I've only just been diagnosed and only been gluten-free for a week (although think I'm having some cross-contamination issues at the mo) so I'm still finding my feet really. How long have you been diagnosed and gluten-free? Did you find that you had to avoid other foods such as dairy to start with as that has been suggested to me?
I have beee Diagnosed since i was 2ish but i gave up the diet when i was 8 due to lack of infomation from the doctors to my parents, but i started again about 3months ago after a spell in hospital i never knew how serious coeliac was i was foolish not to be on the diet for so many years (17 of them). I've luckly not had to avoid dairy but i agree cross-contamination is so hard to avoid especially at work i now have my very own special toaster so i can avoid it. Have you found it easy to switch to the diet?? I did at the start but im getting there now i have even started baking cakes!! they taste so yumm......
Hope your feeling well..