TBH I think it's the people who are very elderly and retired and on only state pensions who are going to be hit badly.
The state pension, without pension credit (top ups) is less than £9K pa. So these fuel bills could amount to 50% of their income. Council tax even for a single person is £2K+pa in some areas even for a small house.
Not an expert here, so forgive me if this wrong, but I was under the impression that if state pension is their only income, they are entitled to pension credit - and should be encouraged and enabled to claim it. That then entitles them to a load of other help, including Council Tax benefit (major reduction - or even all of it?), housing benefit if renting (rent covered?).
Again, I may be wrong here. And tbh even if CT and rent were completely covered, personally I wouldn’t fancy having less than £100 per week to live on after paying my fuel bills.