Your stat is OK, the click is happening at the ~ present cylinder temperature.
That is good to know... One thing that did occur to me but sounds as though it may not be the case is that, in my initial post I mentioned the following:
The boiler is set to come on for twenty minutes each morning to heat the water. Usually, this works as expected and I hear the boiler come on and the pipes knock for around two minutes (which I assume is the pipes expanding slightly, they've always done that). Then everything settles down, the boiler runs quietly and I have piping hot water.
Recently instead of the pipes just making a knocking sound for two minutes, they now do it every 15 seconds so it's almost as though the boiler is kicking in, stopping and starting repeatedly even though that's not actually what's happening, i.e., the boiler remains on for the full 20 minutes.
Thinking about that made me wonder whether in fact, the hot water cylinder thinks the hot water has reached the correct temperature and so is constantly telling the boiler it's up to temperature so the boiler is switching off but then five seconds later sending another message to say, actually it's not up to temperature so it kicks back in again. I don't know if that would explain the unusual knocking pattern in the pipes while they are expanding which it only does for the first two minutes when everything is working correctly.
It sounds as though it is constantly starting and then stopping again over the course of the 20 minutes rather than running continually over the full 20-minute duration and so subsequently it never gets above around 45 degrees.
I don't know if that makes any sense but it almost 'sounds' as though it is coming on for around 15 seconds then switching off because it's getting a false temperature reading but then coming back on again and repeating throughout the 20 minutes.
Having said that though, as far as I'm aware the boiler isn't switching off, in as much as the second green light that appears on the front when the boiler kicks in remains on for the full 20 minutes, at least I think it does, it certainly did when I put it on for 45 minutes, though it did switch off after around probably 35 to 40 minutes, I assume because the water in the cylinder was up to temperature.
iI you like, just switch on the HW just now, take a photo of your gas meter and exactly 3 minutes later, take another photo, we can then see what the coil output is, within reason.
The gas usage on the smart meter is consistent each morning...
I've taken readings over a 3-minute time span while the HW was on but I'm not sure the figures make a lot of sense as they bear no resemblance to my monthly gas usage which is on average 14 to 15 m3 (though that does include some brief cooking on a gas hob) but if I've used 0.134 m3 over three minutes if you divide by three to give you one minute and multiply by 20 to give you 20 minutes and multiply that by 31 for the days in the month that gives a figure of 27.69 m3, almost double the actual usage.
After 3 Minutes - 01317.000 m3
Before HW on - 01316.866 m3
Total Usage = 0.134 m3
The Volume Correction value is 1.02264
The Calorific Value is 39.9
The Conversion from Joules is 3.6