As you (presumably) know, a wall is a Party Wall if it sits on the boundary, even it is wholly on your side. It is not a party Wall if it sits back from the boundary.
You say there's an inch gap. I wonder how you can demonstrate that, because the accuracy by which the Land Registry record Title Plans is not that great. Look very carefully at other boundary features that are in place - are you sure you can demonstrate this?
The problem for you is that he has everything to gain and nothing to lose. If he accepts your wall is back from the boundary, he is going to have to leave a decent gap on his side - making his garage much smaller.
The Party Wall Act allows for the appointment of a surveyor for you - he is going to have to pay for this. Have you appointed a surveyor yet?
I can understand why the Planning people don't want to get involved - this is turning into a Lands dispute, not a Planning dispute.
Be careful people have lost their houses through running up legal bills on squabbles over a few inches of boundary.