Firstly, I would make comment that you've had a bl00dy decent engineer visit you, from the sound of the work he did.
Now then, charging is (as in any business) a
big thing, and we have a duty to do so if it is warranted.
The fact that the 'feed box', (We'll call it a BT99, as that is how it is commonly referred to on various job templates), is on the neighbours premises, isn't all that unusual on estates built around the 60/70's ....... we have many similar set-ups on my patch.
I suppose it was a flip of a coin as to which side the dual-feed BT99 was positioned back in the day, it could as easily have been on your premises ??.
I have to admit, I am not au-fait whatsoever with the charging policies of 2nd lines these days ..... there is certainly a ceiling as to how much OR will throw at a 2nd line install, and the figure going around my head is £1K ?? Please don't take that as gospel.
The problem as I see it, isn't the remedial work from the kerb to the premises ( ie: from the JB23 to the BT99, or JB23 to where the newer style BT66 might go ??) .... the issue is the shortfall of 'pairs' further back the 'spine cable' !!
The 'magic wand' he was using is a 'Cat & Genny' ... basically a tool used to trace where our cables run. He must have identified 'spare pairs' or 'stumped pairs' that are measuring to a buried joint (BJ) under the tarmac you mentioned.
Once this has been dug up, it will become clearer as to whether another 'pair' (ie: your 2nd line) can be pushed along towards the JB23 ??
If this
can be done, I'll put my neck on the line and hazard a guess that all the rest of the work would be soaked up by your ISP/OR ??.
If it proves otherwise ... then from your description above, it would then mean a new length of duct from the BJ all the way to your premises, to provide the 2nd line.
This is where
potential charges may apply ??
Alas, it's purely pie-in-the-sky speculation for the most part, as until the BJ is excavated we won't know what is or isn't achievable ??!!.
Fingers crossed the new 'pair' can be pushed all the way to the JB23 !!!