ProDave

Go and buy something like this https://www.ebay.co.uk/itm/397148477114? That will enable you to test each individual leg of the circuit and identify where the fault is.

I still don't think we know if this heat pump is heating the house with radiators or under floor heating?

You can buy an old style, not calibrated insulation tester second hand on the likes of ebay for not much money that would solve this quickly if intent on doing it DIY.

But you are not going to find which one without an insulation tester. Unless you have the patience of a saint and try the "disconnect one and see if it still trips" method.

Yes, of course the tank will run out of hot water if not being re heated. If you must have 3 showers all in one go and can't change the time you shower, then I really think your simplest solution is change to a different tariff that does not have that hugely expensive period when you most need it.

As above, insulation resistance testing is needed Live to earth and neutral to earth. If you don't have one, buy one, or get an electrician. Clearly there is damp where the wet socket is. It sounds likely there is a lot of damp in the cable as well as just in the socket.

Best of luck with the planning. I fear it may be challenging. Lack of windows facing the view is probably because they had to work with what was there.

Same for me, but I got the impression it was a time delay, so walk slower and they cross closer to the target. But walking the other way and the target is half way between the two crossovers. I use 2 old bucket handles straightened out and then bent into an L shape. I didn't know I could do it until a discussion with my BIL over a pint of beer ended up "Here take these and walk across my yard" and they crossed over half way. "That's the drain pipe from the barn" he told me. I used it in anger when getting my water connection. The mains water was not where the plan given to the contractors showed. They were on the verge of packing up and going away, so I got my rods out and went walking. You could almost hear them sniggering, but the rods crossed over only 1 metre further than they had already dug to so they agreed to go a bit further and there was the water pipe.

Tip No 2. If you have a stud wall that is OSB boarded one side (for racking), BEFORE you fit the plasterboard, cut a hole in the OSB bigger than a socket box. Then cut the correct size hole in the plasterboard once fitted.

It's a personal thing but I like dry lining boxes. Buy the Appleby ones like the picture above, they are good and reliable. Some other makes with different methods of locating them can be dreadful. My top tip. Run socket cables horizontally around the room at socket height all the way round, with a bit of slack in the cable every now and then. Then in the future you can cut an extra hole in the plasterboard anywhere and add an extra socket, you know the one you forgot you might need.

Try it yourself first, I was surprised I can do it. Don't ask me how it works, but it does.

I am keen to see how this back to back WC into a single outlet works, and does it suffer the "swapped contents" problem?

I was visiting a relative recently, she had an extension several years ago with UFH in the extension. But the UFH "never worked properly" so after a couple of years, she had radiators fitted in those rooms and gave up with the UFH. I had no part in that discussion or decision. But following that visit it seems her boiler is set to heat "hot and hard" for 1 hour at a time. No wonder the UFH failed to do anything sensible.

A valid point to make here even stronger, is a Time Of Use tariff should only be used by someone who understands the different charges at different times of day (and with some tariffs they vary day to day) and then actively manages their energy use to consume as much as possible in the cheap times and as little as possible in the expensive times. If you don't do that and just "use it when convenient" I really don't think a time of use tariff is for you.

I don't know your particular heat pump, but there should be a way of setting a timer so it only heats hot water at certain times, and you want to set it so that it does NOT heat the hot water between 4PM and 7PM. Then you will just be using the hot water from the tank and it won't re heat it after use until the expensive period has ended. Same could apply to heating the house, set it so it does not do that between 4PM and 7PM. See if the house keeps warm with the heating off for those 3 hours, hopefully it will.