Flow4 - so glad you posted that - as I knew nothing about such things and was reading Ledkr's tale with horror. We live in a semi (first time with a party wall) and I was entirely ignorant about such things.
I have read through the Party Wall Act guidance and there is no provision for dealing with people who don't adhere to it - astonishing.
Ledkr - now I've read the Act guide (with eyes like saucers) I see that your neighbour is responsible for sorting out the damage, not the builders per se. So it's no good you leaning on the builders - you have to lean on your neighbour and make damn sure they realise it's their problem to fix.
Ergo - the way the Guide reads, you can't instruct the builders to sort it, but you can insist your neighbour takes action. Now. At once. It might be worth printing out a copy of the Guide, and taking this to your neighbour and pointing out that not only have they breached the Act, they need to immediately organise repairs to the damage to your property, without delay. I would be seething at their casual attitude and suggesting that the builders should stop work until the damage to your property is resolved.
I would lean on your insurer too, if the neighbour doesn't fix the damage, the insurance company will have to pay for the repairs and then pursue your neighbour for costs, so the insurers should be being a lot more helpful. I'm sorry you are going through this: one's home is a sanctury and having this breached (literally) would be very, very upsetting.