I haven't read the whole thread (66 answers - *** that) - you say you were negligent. How?
For instance if you allowed the bath to overrun, then yes, without question you are liable for their losses.
If you had an escape of water, for example if your washing machine leaked and you had no reason to believe that it would leak, then you wouldn't be liable for their losses.
For negligence to operate it has to be reasonably foreseeable, using hindsight, that your actions or in-actions would cause a loss.
It is a common misconception that a burst pipe in a flat that causes damage in a flat below makes the owner of the flat above responsible for the damage to the flat below. This is absolutely not the case unless the person above caused the escape of water or knew an escape of water was possible and did nothing about it.