I haven’t played a huge number of live shows, but I’d say that by far the most important aspects are the two things you’ve already mentioned: developing a network of contacts & building an audience.
For better or worse, a decent chunk of the underground / independent music scene runs on social connections - being in the same place as people, developing friendships, and all that stuff. There are bound to be people in your neighbourhood putting on small-scale shows - if you can find out what’s happening around you and start tapping into those little networks, rather than assuming you have to build everything from scratch yourself, you’ll have better odds of making something happen.
In terms of audience - London’s got a million things happening all the time, which is brilliant in lots of ways, but it also makes it really hard to cut through the noise and get people to pay attention to what you’re doing. Playing and promoting live shows can be exhausting, way more than most places, and it’s really easy to lose confidence and burn out.
You don’t necessarily need to have a whole business plan thought out before you start, but I reckon it’s helpful to start by having a bit of a think about who your potential audience is, why they’d come to your show rather than someone else’s, and how you’re going to reach or grow them, then using that to guide your approach to planning and playing shows.