I think it would be best to encourage DP to talk to the landlord about it - mainly because if you leave it too much longer and don't contact them, it may become evident that you knew there were white ants and failed to inform them leaving you liable for part of the damage. I don't want to put more pressure on you because you sound like you are having a horrible day and it is very stressful.
If it is obvious that you know the damage is there and don't act, allowing the damage to continue then you could be held responsible for the damage that occurs from when you did know.