I had a rather strange experience concerning a neighbour when I lived in Wiltshire,UK ten years ago.
This neighbour had been considered a friend, and been to barbecues at my home, and vice versa. Anyway, I returned to my home from working away for the week, to be confronted by him telling me he owned the piece of land between my garage and his house (gable end).
He'd lived there for about ten years, and it had never seemed to enter his head, but I later discovered he'd tried the same game on with two other neighbours whose gardens abutted to his garden. I spoke to my lawyer who wrote a letter on my behalf refuting the claim, having spoken to a previous owner of his house, (plus I checked plans etc., all in support of my position). When I tried to give him my lawyers letter he refused to accept it and closed his door on me, but it was the last I heard about it.
I had my own back a few years later, when he came to tell me he'd sold his house and was moving out, and I completely blanked him, in front of a young neighbour from the other side of my property, (she only laughed when I explained my actions to her).
The point of the story is I'd guess the OP is being tested by the new neighbour, and in all likelihood they've done similar things wherever they lived before, but it may not be a job for lawyers just yet, and other approaches described above by other forum members may be the way forward.