Party Wall notice advice

Jonosss

Hi
Can someone please help? We have just had planning permission granted for a modest extension granted. Our neighbours have been sent unsolicited letters from a well known Party Wall Notice company discussed in these forums previously.

My neighbours naively responded to them and letters have been sent to me.I am choosing to ignore letters from this company as I aware that it is only us, the owner builder, who can raise a notice.

I do not believe we are doing any work that requires us to issue a notice and I understand the citeria for excation work within 3m and 6m of their buildings.
Questions I have are:

1 - They have a building, conservatory, within 3 metres of where we will be excavating but on their own admission the brick work for this has unbelievably been built straight onto a standard garden patio and is not on any foundations/footings. Therefore I am assuming that because there are no foundations for this building in question the depth of our excavation is non notifiable as there is nothing of theirs to match to. Is this correct? That aside it is they who chose to build the conseravtory without any footings.
2 - A second letter from the company our adjoining neighbours responded to has arrived. Using threatning language, saying that they have been informed we intend to commence building work shortly and that if we do we could be contravening the Party Wall act etc etc along with other threats of court etc. I am choosing to ignore it, we did not raise a notice and have no intention of doing so. We did not appoint them so should I be concerned about ignoring their threats? We may commence non excavation work soon.

Thanks in advance