Who is Responsible if wall is damaged or falls down.

A garden wall about 6ft tall has a settlement crack in it for years, if bord gas networks make a gas connection and as a result their work disturbs or causes damage to the wall or it falls down (worse case senario) are BGN responsible.

Proving who did what to the wall is always a bit tricky.

On the off chance that the wall is a shared wall, the following link might help.
http://www.irishstatutebook.ie/2009/en/act/pub/0027/sec0043.html#sec43

Its a boundary wall not a party wall, am going to take a few before and after pictures just in case.

Depending on how bad the crack is, you may need to consider this from another angle. If the wall falls down due to an existing structural fault that is known, and injures someone, who is liable?