How long have you been together? How do you see the future? I take it you don't have children?
I think this is the level you need to move to mentally here. Let's cut the crap, he has stepped way over the line, that is not up for any sort of discussion. He will want to make it the discussion of course, because then you can focus on hair-splitting over whether he should have mentioned you earlier etc. But none of that is the point. He's disrespecting you, sending out all the wrong signals, letting another woman corss boundaries right left and centre. He's either a cheat in the making, or a complete arse - either way, the ONLY way to actually sort it out is to nip the whole thing in the bud by being zero tolerance.
So the real question is do you want him. Do you want a 'him' that thinks this kind of behaviour is ok, and puts a lot of energy into defending this kind of nonsense with another woman? I wouldn't, my respect for him and enthusiasm for being his partner would be heading out the door right now.
If you really want him, you can give him an ultimatum and hope he makes the right decision.
If you don't particularly want him, I'd just dump. Sound hasty? No, not really. This is a huge red flag for the future. He likes what's happening at the moment and he isnt' stupid, just pretending to be. So even if he has no intention of it going further, this is a hint of the annoyance and misery and paranoia you will be signing up for by staying with him.
I would suggest telling him this. You have no interest in being with the kind of shitscrape who leads this kind of dance. He makes his mind up what he wants, or he can ship off right now and stop getting on your tits with all the flirting.