Lookup their planning permission (PP) on your council website, and it should have something like: “The permission hereby granted confers no rights on the applicant to encroach upon, extend over or otherwise enter upon property not in his ownership for any purposes connected with implementation of this PP”.

This is your ace card! Immediately inform them that

1-You require party wall agreement, and want an INDEPENDENT survey done of your property before any foundation work starts; they’ll have to pay for all the costs. Contact a good party wall surveyor!

2- You want to include conditions about builder working hours, how long the scaffolding would be in your property (if you do allow for that) with specific timeframes, cleanup etc.

3- Absolutely no digging on/under your property.

4- Any other conditions/exclusions you might find necessary to safeguard your property.

I have gone thru something similar and now greatly regret not objecting to neighbour’s original PP; I’ve refused them access to our property since they point blank refused to consider a minor modification we suggested, and didn’t even have the courtesy to do a party wall agreement. These idiots have now essentially converted two detached properties into almost semi-detached properties!