how would this work then?

[whatatwat]

we are having a conservatory put on. its going to run along the same length as the neighbours extension.
we have asked them if we can attach to their extension, they dont know if they are ok with it yet.
they are asked us to look into having the structure totally seperate.
that means there will be a tiny gap left between our wall and their.
they are also worried that by having this gap, they are now going on that they are worried that this could lead to damp, or water ingress or mice or fairies who will steal children. and that even if we have it seperate they want us to promice to make their wall 'safe' and that if there is any issue with their external wall in the future we will allow them to access it from our side...
are they mental? or is this common?

Is there wall along the boundary? If so, I think you have a right of enclosure (ie. you can attach your structure to it) but you have to pay them some money for the shared use of the wall.

their not there

I think it runs along the boundry, I'm even more sure their roof overhangs the boundry.

I think you should try to establish whether their extension forms part of the boundary, then that will give you rights to use it.

Ok, just had a look at out planning applications, it looks like their extension forms the boundry.

In that case, google party wall act and get in touch with a surveyor. Essentially, if they have built on the boundary, then you have the right to build your structure using that wall.