As you probably already suspect, I think it's a great idea
I see 2 markets: 1 is an alternative to renting an office. The monthly fee will suit those people but not someone who is only in Brum for a meeting occasionally and when you are competing with a coffee shop which is free.
Have you worked out the relationship of this service to membership fees and WiFi access from the library or members rooms? Do you want to use hot-desking to boost membership or as an income stream, like room rental?
If I'm going to an evening Meetup that starts 6pm+ but I catch a train before 4 so the price is lower, I'd like somewhere to call in and get some work done, preferably with a cup of coffee, but the tea room closes too early. The library and members' room are fine but don't have many power sockets but as an out-of-town member I can get that for 50p per week and hardly have to think about whether I should renew, even though I've only used it 3 or 4 times so far.
It would be nice to meet up for an informal chat with people from this community without organising a fully-blown meeting that needs rooms with projectors etc. but most of our Meetups don't charge anything so there is no-one to pay the fee. Such chats might require a different space, separate from 'the quiet room'. It overlaps with your room-hire model.
The last couple of requests I've seen were people coming in for a day and wanting somewhere to work. The original Internet Cafes were access for an hour or two per drink. What about contactless card swipe-in for a fee, for a limited period, with an optional voucher for a drink?
We have meetings in pubs and offices around town that could bring new audiences to your building and I think there are members of the community who would be willing to talk to new audiences about tech in a fun way, rather than only talking to each other, e.g. to school parties to give you new income streams from meetings, in return for your building feeling like tech's home in the city centre. I might be wrong, so please speak up if you'd do a talk to a general audience where you weren't trying to sell your warez. There might be funding available for such 'hubs'. There seem a fair number springing up.