Hi Neil!
No need to be worry about. Just see the people, look their faces: someone is paying attention and listen, someone maybe not but it doesn't mean they are not listening. Just do your gig and smile at the ppl who look at you. Before to start a song, talk to the crowd, as you were among friends. Because
they are your friends, in that moment, even if you doesn't know anyone, in that place.
Relax yourself: they went to see you and listen what you have to offer.
If you are relaxed, the people know it, they sesnse it. If you are nervous, but keep nice, they can forget the fact you are nervous.
Think about this: who would you see in a scene, somenone who is a nice person and tells something interesting (and play good) or a sort of bear that doesn't want to communicate?
This is one of the "secret" of the scene: communicate. No matter what happen, even you make a mess with a song. Be nice and friendly and the ppl will follow you.
In the pause (if you make one) go through the tables and smile and talk with whoever wants to say something to you.
A mistake on the scene can happen and it's "normal": we are humans, not machines but just keep go on and play. All will be ok.
You know? All will be ok because all IS actually ok: ppl are coming to see you, to listen what you have to say. They want just relax and listen something nice. Give them it.
You can, between a song and another, talk to them. Is not important what you say, the important thing is to keep communicating, nice and politely.
Last: sorry for my terrible english, but i hope you got the idea inside my writing...