Tiled floor type wet room.
That's a big part of your problem then.
You shouldn't really have a tiled wetroom on the ground floor like that
unless you have a metallic grid in the concrete floor that's bonded to the main earth terminal of your supply, especially not with a PME earth as you now have. The problem is that the concrete floor you are standing on with wet feet is inevitably going to stay at true earth potential whilst the rest of the "earthed" stuff in your house (including your plumbing) bounces relative to it. Essentially your feet are outside the equipotential zone. Technically the DNO should have refused to provide you a PME earth terminal because of that wetroom (hopefully your electrician didn't just connect to their neutral or cable sheath!). The whole safety case for PME hinges around maintaining an effective equipotential zone so the "earth" terminal they provide occasionally wondering up to a few hundred Volts doesn't kill people, hence all the worries about using a PME earth terminal for outdoor things like car chargers.
The best improvement you can make here without digging up the floor would be to put insulating sections in all the plumbing that enters the wetroom, so you can't get a dangerous shock off the water pipes whatever voltage they are at. You should also seriously consider reverting to TT earthing.
These symptoms from a fault 12 miles away are a bit odd though. It is possible that the HV and LV earths are combined at your local substation (which will be a few hundred metres away at most) but this is only done when they can get a good enough connection at that point to hold the voltage down (to some hundreds of Volts) during reasonably foreseeable faults (it could of course have been an unreasonable fault). Did you say it was a pole mount transformer? It would be unusual to have combined HV and LV earths then because it's difficult to get a low enough earth resistance in the limited space. It is possible that something very weird happened, with like a 132 kV line at a major substation falling across an 11 kV output and raising its potential enough to flash over 11 kV : LV transformers all over the place. It would still be odd to get so much rise of earth potential so far away because it would flash over in huge numbers of places giving multiple parallel paths to ground.
For the rest of you who are not UK based, earthing in the UK generally falls into the following categories:
TT. You have an earth rod that is your property and gives you an earth reference. It's generally got a resistance of a few tens or hundreds of ohms so RCDs (GFCIs) are mandatory.
PME / TNC-S External to your house there are four wires. Three phases and a combined neutral and earth conductor (CNE). At your property this splits out into earth and neutral. The network is supposed to be designed with high reliability connections on the CNE conductor (multiple redundant crimps, etc.) and with regular earth rods throughout its length. This gives you a nice low impedance for tripping MCBs on earth faults, and people tend to notice when the neutral fails so it gets repaired quickly, but when it does fail your "earth" can go up to full line voltage. It can also sit 10 V or so from true earth in normal operation which can then divert lots of amps down any earth connections you have such as plumbing. Sometimes electricians create this connection on networks that don't have the extra earth rods and double crimps, needless to say this is a Bad Thing(TM)
TNS - There is a 5th connection back to the substation providing an earth connection separate from the neutral, often the lead sheath of the cable. They repair these types of networks with 4 core cable, so in the modern world you should just treat this like TNC-S as all the same risks can then apply.