Hi from a fellow ‘Cheltonian’.
I liked your post very much – the assumption that you ‘ought’ to introduce yourself to people or that you ‘ought’ to know each other creates quite a powerful frame.
My (similar) way of approaching these kind of situations is to ‘imagine you’re the host’. Back in the day, I've used this tactic fairly effectively in the legendary Retreat (legendary if you live in Cheltenham, that is ...)

e.g. ‘Hi, I thought I’d come and be sociable / be polite / say hello for a few minutes’ (the ‘few minutes’ bit gives you an inbuilt FTC)
or even just ‘Thank-you for coming’ (perhaps with a compliment about adding ‘glamour’ to the venue).

You’re right that this enhances your status and is all part of ‘taking control’ in social situations. In my AFC youth I would have followed this up with the offer of a drink but now I know better ...
This works fine even if you’re in a place you’ve never set foot in before, but the converse role is the ‘stranger in town’ seeking local guidance – which can also work well.
Good luck and keep the flag flying.