Sorry for the late reply but the West Midlands Police Sports Club is a very good site for Birmingham city centre. The site itself, the
Tally Ho, is a number of rugby pitches near to Edgbaston cricket ground. (Twins only.)
The guy in charge (the name escapes me, I'm afraid) is also a very nice chap and is very helicopter friendly (as long as you don't land on his 'square'!)
You should be able to get their contact details off their website:
http://www.westmidspoliceclub.com/en/
HTH