Oh good grief, get over yourself.
"You have already done something that could - if you have been badly advised - cause damage to your neighbour's property. Digging a hole where you have dug it could have destabilised the wall. If you have acted reasonably it won't."
Digging an exploratory hole to determine how far down the foundations go is not going to cause damage to the party wall.
"Your neighbour is justified in investigating what you are doing because he has nothing apart from your verbal assurance that all will be well. That butters no parsnips."
What exactly do you mean by "justified"? He is certainly able to ask the OP what she is doing but he is certainly not entitled to demand anything of her.
The law in this country is that unless building work requires a written notice then nothing in writing is required. PPs here have just said that it might be beneficial, as a courtesy, to inform the neighbour in writing what is happening.
But she certainly isn't required to in any way at all.
"So you give him a signed statement... blah, blah blah, load of unnecessary rubbish that is not required"
Just as an example of how bad this paragraph was:
"...including all relevant evidence if you are given professional advice that the work is too minor for the Party Wall Act to apply."
The Party Wall Act very clearly states when it applies and when it does not. "All relevant evidence", really? All it needs is a simple statement from the OP saying
"Hey dude, I'm digging down no lower than the foundations of the wall"
In fact, she doesn't need to even do that. She doesn't need to do anything at all in that situation. In this country even that sort of information isn't required.
People here are just saying that it might be nice if she does it just out of courtesy.
"Your neighbour gets peace of mind knowing that if you break your written promises and use a cowboy builder who doesn't do things properly, don't bother with the structural survey, or do anything that causes damage, he can (and should) sue the pants off you, and that letter can be used as evidence against you."
If the OP does anything that affects the neighbour's property then, yes, they can claim for damages.
"...and that letter can be used as evidence against you."
I'm sorry, but for evidence of what? If the OP were to spell out in excruciating detail what her plans were, what difference would that make?
In this country there are strict rules on what work can be done on boundaries and what work needs to be notified to different parties. If the work does not need to be notified then the OP is under no obligation whatsoever to notify her neighbour.
People here have just been suggesting that she keeps her neighbour broadly informed of the nature of the works that she is planning to undertake just as a courtesy.