Just adding the pictures of the back garden.
I've been following this thread, and there are two problems. You have the attitude that you can do what you like and your neighbour has to put up with it, very wrong. I'm a reasonable person but if I was your neighbour I would now have a very hardnosed attitude towards you, ie I would give you nothing.
You have created this mess and you deserve all you get, I feel sorry for your neighbour.
What would you have done differently ?
Yes, I have to say I agree your attitude is coming across poorly as being entitled. In particular, as the other chap pointed out, when you buy a property you buy it as is. If your neighbours signed a party wall agreement, then sold the house, and the new neighbours said "we didn't sign the agreement! We've just bought the house! And actually we'd prefer it if you lowered your roof back to what it was before!". Would that be fine with you because they "had just bought the house"? What if they asked you to pay for it too!? That is literally your argument, and it is weak. Bottom line you want to do work that affects them that they don't feel a need for...so to start off with a position they should pay because you deem it benefits them somewhat? No wonder it has gone down this road with neighbour reacting.
Now, instead of taking a step back and re-adjusting your approach it looks like you'd rather shoot yourself in the foot with a separate wall, smaller space, and the effort of suing them over drainage. You come across to me as spiteful.
The ONLY thing I've read of your complaints that has any merit is the drainage. That would annoy me too, but you really should ask if you are going the best way about resolving it. Even here, depending on how long this has been in place, they may, as a previous poster noted, have accrued common law rights to continue draining into your property. That may sound nuts, but it is how I remember the law. So you could actually lose the action you plan on taking. I'm not certain on this point - you can spend money on a lawyer if you like - but it is my recollection.
I don't even understand what you are suggesting with adding an extra roof, taking felt off and leaving a gap etc...but just hearing it makes me think I probably wouldn't want it either.
As others have said; you may not hear this but the best way forward is to:
a) reset your attitude and re-engage your neighbour
b) cover the cost of everything, and imagine you were your neighbour (no bodge jobs with extra roofs and felt gaps - something YOU would want in their position).
c) Outline things clearly and simply so as not to fluster your neighbours into thinking they need all this extra advice.
Can I ask, where did your garage roof drain to, before you removed it?
Looking at the photos - has somebody actually 'designed ' ( using the term loosely ) all this ,what is going on
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