My reservation would be, they are not really up to switching a 13 amp load
This is also my thoughts, but maybe only a 13 amp plug, and not using 13 amps.
My flat was also all electric heating/cooling, using one of this
type of heat pump to both heat and cool, which sat in a box built into the window. In my case mainly cooling, flat was in Hong Kong, but if you want, then heat pump heating and cooling is possible. There are versions not needing the box
but what we are looking at is cost, storage heaters
are around the same price as heat pumps, so for a whole install likely looking at a few £k, but what is more important is what power comes into the flat, and how much is needed for non-heating use.
My own house, no gas, but I do have room to store oil, any central heating is oil fired, I also wanted to reduce the bill by controlling when and where heating is running, in my case, the problem is the time it takes to re-heat the room. It takes around 2 - 3 hours to re-heat my living room, basic problem is the radiators are too small, I have a 20 kW boiler, but can't use all that power, likely you have the reverse, if you need 24 kWh and your supply is 60 amps, (13.8 kWh) of that, half needed for other than heating, then you have 6 kWh for heating, so to get that energy you need 4 hours, these figures are a guess.
So there is a lot of working out to do, both cost and what can be done. But also what is required, there is a vast difference when arriving home at 6 pm, bed 11 pm and up and out 7 to 8 am, to being retired and living there 24/7.
