So far, the house has been comfortably warm when I get home. The door to door journey is about an hour, although yesterday, I stopped to talk to some colleagues before I left work and after I had turned the heating on and then took a long walk before getting on the train, so the house had even longer.

Sunday: heating on all day, average outdoor temperature 9.3C, heat curve 0.50, 4.3kWh consumed, reported COP 3.2

Monday: heating off from 1100h - 1700h, average outdoor temperature 9.9C, heat curve 0.45, 3.2kWh consumed, reported COP 3.3

So far, those tests appear to show that that claim is not correct, at least in the case of the conditions in which my heat pump operates. This, in turn, suggests that it is not wise for anyone to assume that this claim is true for them without also testing it. This may be reason at least to be somewhat sceptical of other, similar claims, such as that it is better not use TRVs and also test those claims before acting on them.

I will continue to document my findings here lest my findings so far cannot be replicated over the long term. I should encourage others alsoyto test this claim with their own setups.

Thanks for doing so.  We do need more data on this and many other things because there are lots of variables only some of which theory can currently take into account.  This week is a particularly good one for such tests (in the south of England anyway) because we have several days in a row when weather conditions are very stable,  something that happens only rarely.

That said, until we have robust data to the contrary, the guidance based on theory is, i would suggest, still the best starting point for most that we currently have.  Many won't be bothered (or won't know how) to run proper experiments and so we do need a way for those, perhaps the majority, who aren't very interested in the detail of heating, to procede.

Keep posting!

So far, those tests appear to show that that claim is not correct, at least in the case of the conditions in which my heat pump operates. This, in turn, suggests that it is not wise for anyone to assume that this claim is true for them without also testing it. This may be reason at least to be somewhat sceptical of other, similar claims, such as that it is better not use TRVs and also test those claims before acting on them.

As to leaving the heating on being beneficial, I do not quite follow that.

I presume that you heat your hot water at times you are not taking a shower.  Just like your hot water tank your house stores energy.

The only benefit would be less need to add more heat to the house

Not quite.  Because you would be heating over a longer period you could do so at a lower flow temperature which makes your heat pump more efficient, so you can deliver more energy to the house for less money.  The trick is to balance the time and the efficiency.

28-32C seems to be the commonest range of flow temperatures at present, although that might increase a little as the weather gets colder.

This, and your consumption, is low that most of the assumptions dont apply because the basic thermodynamics (which argues unequivocally for low and slow) is dominated by the engineering factors (which we cant currently calculate).  This means you have to do the experiment.

However what I would say is this.  At present your electricity consumption for heating is very likely one half to one third of your total electricity consumption and you may well be better off by concentrating on the other two thirds rather than getting too obsessive over heating.  Obviously I don't know your lifestyle but typically a house consumes 3500kWh/year of electricity without heating.  Thats your electronics, refrigeration, cleaning, lighting.  This equates to a UK average 450W per household, whereas your heating is currently 150W.  If you want to reduce energy consumption (which is definitely a good idea) you may want to look also at the things you leave on overnight.  Several 'low power' devices each consuming 25W may well be more than your heating!  Obviously this balance will change as it gets colder but in most of the UK its actually quite mild for most days.

Please dont take this as a criticism, many on here (including me) admire the low energy use of your heating.  All Im doing is reminding you that you use (and pay for) energy for other things also and, once you get to the admirably low figure you have for heating, its worth taking stock of what else matters.