Well at the moment their electricity bills are £3 a day.
Assuming 5kwh of that is non heating and 1 kwh is about 25p, they use 12 kWh a day in total of which 7 kWh is heating. If you install a heat pump and get a COP of 3 then the 7 kWh reduces to about 2kWh producing a saving of about £1.25 a day or £450 a year. Of course there is no guarantee the saving will be that much as standard electric heating is more flexible than heat pumps as you can turn it off in individual rooms and flick it on and off as and when you need it.
If you assume that the total installation is about £10K then it will barely cover the base interest you would get on that £10K. And that is without stuff like maintenance as well. Even if the thing lasted long enough (unlikely as heat pumps have powerful fans which as moving parts are prone to replacement) it would take 20 years to recover the basic install cost, which no commercial enterprise would even consider as an investment return.
It doesn't sound like the OP is that unhappy at the moment with their existing system (whatever it is), they don't have huge bills and there is not that much carbon to be saved, plus the install of such a system is risky, disruptive and probably takes up a fair bit of extra space in their house, so probably just stick with that instead.