Part 1 - the gushing water
Coming to my senses, I realised that no header tank has any business to be refilling in the middle of the night when no one is using any water. Earlier that evening, I had removed the toilet, radiator and other water-related things from the WC, so I thought it prudent to take a look downstairs.
During the night, one of the (disconnected) thermostatic radiator valves had started to leak water; which was now gushing all over the place where the floor would have been, if I had not removed the floor earlier that evening too. So now it was just gushing fairly harmlessly onto the concrete sub-floor.
I checked that the thermostatic radiator was set to "0" (off) and then managed to tighten the thermostat a bit tighter onto the valve which stopped the water. So, I let the water system fill up again, ran the pump for a bit and bled the radiators, before checking that there was no further leaking and returning to bed.
Just as I was falling asleep again, could I hear a header tank filling up...?
Part 2 - A mystery solved
Some time ago, I fitted thermostatic radiator valves to our radiators. They are easy to fit and apparently save you money. However, they came with an extra bit. You can choose whether to screw the thermostat onto the valve, or you can choose a normal non-thermostatic "tap", like the old valve that I was removing.
At the time I didn't understand why I would want this extra bit - the whole point of the product was that it was thermostatic. I kept the bits anyway (I'm like that).
Perhaps it was the fact that I was now shivering in my dressing gown and slippers, standing on a soaking sub-floor that was at outside temperature in January that made everything finally fall into place.
What is that extra bit for? It's for when you don't want the thermostatic radiator valve to be thermostatic, of course! For example if there is no radiator connected to it and it's freezing cold because there's neither floor nor heating. On a thermostatic valve, "0" does not mean "off", it just means "very cold". So when the temperature really gets very cold, it turns the valve on.
So, I grabbed the non-thermostatic extra bit, stopped the water with my thumb while I switched it over, and of course it turned the valve off properly. I let the water system fill up again again, ran the pump for a bit again and bled the radiators again, before checking that there was no further leaking and returning to bed again.
And the moral of the story?
You can bleed radiators in the middle of the night without waking up the household.