I am very surprised that you state there is "a growing body of irrefutable evidence that Heat Pumps can work" when clearly they do not even when they are set up to the correct parameters. A vented or condenser tumble dryer takes 90 minutes to properly dry clothes. A heat pump dryer takes double the amount of time so does it really use less electric?
If it uses less than half the power during the running period it uses less "energy" & that's what you are charged for on domestic tariffs. So that would be "less electricity".
If we had our heat pump set to 20C it would be running all day to keep the temperature at 20C and it would have to work harder on really cold days. On really cold days it resembles a block of ice and goes into defrost mode. When running in defrost modem the heating in the home shuts down same as when the hot water is being heated up. When the defrost has finished, the home is a lot cooler and again the machine has to work twice as hard to bring the temperature back up again.
This to an extent implies the unit is undersized for the application as it is forced to drop to a low evaporating temperature. There however has to be some drawback with air sourced heat pumps in environs that are simultaneously high humidity and near freezing, where to counter icing up unit size would grow significantly.
Secondly if the house temperature drops "a lot cooler" during the defrost period so quickly, then the house is poorly insulated, suggesting not a suitable candidate for heat pump technology. But, also one that would have required more gas than a more insulated home.
How is that efficient as that applies to all heat pumps? In the meantime your electric bill is rocketing. We are looking at an electric bill that is going to be north of £300 for this month! Remember that we only have the temperature at 20C between 6-9am and 4-10pm. The rest of the time it is at 17C. In summer our electric bill averages at about £100 per month.
Being "efficient" is not the same as being "effective".
The cost depends on how much we pay for energy we need to buy in.
If you were heating on gas, then presently we pay considerably less for daytime energy quantity than we do for electricity.
With a heat pump, it gathers a significant part of the energy needed to heat the home from outside, thus requiring buying less energy in, however its the more expensive per unit electrical.
With gas all the energy needed has to be purchased.