I once had a similar property, the corner house was undergoing extensive renovation that needed such a consent as it involved pilling and also from a single storey to a double storey.

The things to consider :-

1) How close to your property would the pilling and footing be done. I would request for what type of pilling would be utilised, how close to your property especially in regard to the firewall.

2) Direction of the sunlight and whether the structure would cast a shadow on your property.

3) Roof design, guttering and air conditioner water discharge plan especially if there is a shared gutter. Would the roof design cause water to flow onto your side thus creating noises and or leakages.

4) Are there any windows that later could be used as a platform to view into your house.

5) Access to your side of property for maintenance issues such as painting the walls etc.

Finally last but not least verbal agreements are worth less than toilet paper. Anything with regard to damage no matter major or minor must be in writing.

Nope I didn't give consent and neither did the neighbour behind him.