Sounds like your neighbour's a selfish sod!
Well they recommened before you do any work of this type, that you make agreements with your neighbours regarding the work you are going to undertaking. Idealy you want it in writing, you can serve notice on your neighbour informing them of the work that you are going to do and they have a period of 14 days I think to appeal against it.
It's a tricky one, because you already know they're not happy about this!
This is what i'd do, get a structual engineer in to do calculation, inform building regs of the work you intend to do, they need to notified at some point anyway. Inform your neighbour that this is what you are doing, and that everything is being done correctly and to the regs. Hopefully reassuring them that it will not effect thier property in anyway.
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