Side extension - Boundary dispute -Party Wall Act?

[noseall]

Glass half empty

No. Just building nous. And the reason many architects chose not to design extensions that are built right up to the boundary

 

[wessex101]

I think this is where the idea fails. Usually resulting in permanently wet or spalled or effloresced brickwork.

It is rather sad that neighbours can't get together and agree a mutually beneficial arrangement. It is possible to build a parapet wall detail on the boundary or a tapered box gutter that doesn't allow rainwater run off to spill down the face of the wall.
From the photos the OP hasn't got a lot of room down the side of the house so by the time you've got and external wall probably 300 - 350mm thick and you leave a gap say 150mm the extension will be too narrow to be of any use.
EDIT: And what exactly is anyone supposed to do in that 150mm gap. It is of no use to the OP or the neighbour so what is the point?

 

[noseall]

It is rather sad that neighbours can't get together and agree a mutually beneficial arrangement.

Not especially sad, but reflective of how combative or protective some folk are. Designers should not work on their own personal expectations.

EDIT: And what exactly is anyone supposed to do in that 150mm gap. It is of no use to the OP or the neighbour so what is the point?

Call it a DMZ of buffer/safety zone.

 

[jj4091]

And yet that is exactly what the neighbour has done with his car port and fence and now expects the OP to leave a clear gap so he can have access?

How do we have semi detached houses and terraced houses if building up to the boundary is so problematic.

The OP should build up to the boundary. The design should ensure the wall requires no maintenance and has no overhang to cross the boundary to avoid potential disputes in the future. In fact my preferred option is, with the neighbour's agreement, to build astride the boundary so that the neighbour has the option to use the new party wall in the future if they wish.

Semi detached and terraced houses are bought as just that, and no access along the boundary is needed for maintenance so that is a bit of an irrelevant reply.
The neighbours car port and fence can be maintained from his own side in the main and it appears the OP has had no issue with it until he started to look for something to nitpick about.
I know of no type of wall that will never be maintenance free.
He is not getting the neighbours agreement - thats the problem.