Hi kitatrob
Welcome to the forum, The young amaze me (I'm assuming you are young) do a days work and want to go down to a gym. When I was young and I came home from work it was all I could do to manage to get myself down to the pub.
I have never heard of a 24 hour Gym in Birmingham and I certainly have never of one in Birmingham, and by the way that would be Stoney Lane, Sparkbrook, Yardley or even Northfield as there is no Stoney Lane in Tyseley.
Have you tried one of these top end hotels that have their own gym and pool. I have no idea how they operate these places never having entered into a fitness suite in a hotel. Do they allow members of the public into them? Its worth an enquiry.
Phil