In the UK, incoming water and gas have been plastic for decades, since at least the 80s.
In a good few cases. My water supply (in UK) still comes via metal pipes in 2025, as does that to everyone else in my village (but we have no piped gas supply)
In the TN-C-S supply, which I assume is what I have in the UK...
By no means everyone in the UK has TN-C-S. Indeed, it was only a few decades ago that no-one in the UK had it. However, from what you describe, your supply is being used as TN-C-S - so, as I said, let's hope that the incoming distribution cable has been PMEd!
, the E only exists as long as the supply's N is intact.
Yep - although there may also be additional paths to earth via bonded metal supply pipes,like the ones that you imply you do not have (although many people do).
If incoming N gets disconnected, then the house has no E - EXCEPT random, undetermined paths, some of which could be someone taking a shower.
There should NOT be any 'undetermined paths to earth', and if there were then the installation would not be compliant with regulations - all possible extraneous paths to earth ("extraneous-conductive-parts") should be identified and bonded the the house's 'earth'.
Ironically, if your person in the shower somehow touched a live conductor, they would NOT receive a shock (and no current would flow through them) if nothing in the house was connected to earth!
I think the addition of one or more earthing rods would provide an extra layer of safety.
As I said,it will do no harm, but nor will it do a lot of good. As above, and as I said before, the most important thing is that all extraneous-c-ps are bonded to the house's 'earth', so that there can be no significant potential differences (which could cause electric shocks) between any two simultaneously-touchable metal things within the house.
What you you feel that an earth rod would protect you against, and how?