I'm currently dealing with the same issue and it's highly frustrating after building Overdozer under a gazebo it's basically been top priority to get something sorted.

An idea I explored initially was seeing what the local council provided - mine does garage sites (where you erect a structure on the plot) and lockups - more like a garage but often under waiting lists. Though naturally they'd require a generator and security would be somewhat of a concern, as for the noise of a generator you could build a baffle box that will dampen the sound considerably.

Also looked into Gumtree for workshop spaces but these often run very expensive and that's not idea.

I'd go with what people have suggested though - looking into hackerspaces, they're small and usually well kitted out plus full of very knowledgeable people. Another option I've also looked into is looking for a local model engineering society/club.

In the end I've managed to strike a deal with my Grandpa to clear a plot of land and erect a shed.