I'm sure your barrister will conclude that you have a strong case and he has an extremely weak case.
However, they will never tell you with certainty that you will win and they do usually advise settling outside of court.
I think he's bluffing. I would not agree to give him anything and I would tell him to go ahead and sue. Unfortunately, it is a game of chicken.
I've been there and I didn't back down. I had evidence in writing. All the other side had was her opinion, nothing in writing, nothing substantial to back her claim so she backed down.
If you have evidence in writing, including evidence of your aunt not living with him, it will be relied upon much more heavily than someone else's uncorroborated word. So it doesn't matter if he's told people they were in a relationship because he has nothing in writing to back that up. He could have just made it up, which in this case, he has.
Judges aren't stupid, they are able to assess the most likely version of events.