Assuming you have working fireplaces, as we have had in all our houses going back 45 years, there's an easy solution.
Many people seem to overheat their houses; in houses where we had CH, the stat was set at 62F/16C. Now we heat to about low 60s, a bit vague as we have storage rads and woodburners.
Also, it was routine to heat one room. Many people seem to think they should be able to wander around the whole house in their shirtsleeves. How wasteful we are.
I would be more concerned about the fridge and the freezers. I have thought about a back-up power solution with a small petrol generator, but I would run a separate feed to the appliances I wanted to keep going. Putting the power into the CU and just hoping that no one will turn on too many appliances is too woolly for me.
In practice I think the brunt of any cuts will fall on industry, or what little industry we have left. The last thing the politicos will want is voters being left with no tele.