With my parents house as with many of that age, the earth was the water supply pipe, when the water main in the street was renewed with plastic this earth became ineffective, so when the wet room was fitted this was found out, and the electric supply authority was phoned and asked what earth they should have, and they were unable to answer, so sent some one to investigate who fitted a TN-C-S earth system.
With the house in question with this tread it could be the cut wire is a bonding cable or an earth cable, from pictures there is no way of knowing.
If a bonding cable then really it should be extended to after the water meter and reconnected, reason for after meter is if meter removed the pipe work is still bonded.
If it is an earth cable, then alternative earthing system needs to be found, as using the water pipe is not reliable.
Since which earth system is used is down to DNO in theroy you can simply phone them and ask if your house has some outside item earthed, and your neighbour also has something outside then unless both earthed with same system one could get a shock touching both (although unlikely) so the DNO has to decide what earth system, they don't need to supply an earth, but they do need to say what earth is used.
So if DNO says earth is TN then water pipe is not the earth, but bonded, if they say TT then you need to look for an earth pit, in real terms I would not trust a phone call, so I would want some one with electrical knowledge to check.
A photo of the incoming supply may help, it may be clear as to type of supply, the person fitting water meter should have checked if earth or bonding and it should have been connected, but we don't know where, so maybe neither did he, for all we know he may have reported he had not connected and why.