You’ve tried the battery and Invertor idea I take it ? Lol
Yes, it was expensive, and I will admit that, but not fitted solely to power the central heating and freezers, there are other benefits as well, and it does depend on when we get a power cut, time of day and summer or winter. The software holds 10% of the battery back for the UPS function, and the battery is 6.4 kWh so 640 watt/hour at worse point. So around 5 hours it will keep heating running.
Should the power cut be when the battery is fully charged, then likely the solar will keep it topped up for weeks, clearly any repeat of winter of discontent, and we can change how much is held back.
A petrol inverter generator would be the best idea to keep heating running, and with that in mind better if the boiler is plugged in, not connected with a FCU. The generator does not need to be big

so that one would do.

at nearly 9 kW, still not sure if that would run a heat pump, likely you would need to use convector heaters in key rooms, so in real terms it would need to be one of these

which to be fair is not too expensive, also need to rent the bottle of course, but they do make the home damp. Last house, something more like this,
but we had mains gas, this house has an open fire, so we could burn wood, and we do have loads to burn. In the past, we had a caravan, but now we cross fingers and hope any power cut is when batteries are reasonably full.