I actually think this could be a reasonable course of action.
Fuel poverty is defined as spending more than 10% of your household income on fuel.
So how about people refuse to spend more than 10% of their own income.
If your income is £1000 a month, pay a maximum of £100 or all your bill if this is lower.
If your income is £2000 a month, pay a maximum of £200 or all your bill if this is lower.
etc etc.
That means that lower income households are kept out of fuel poverty and higher income households will still probably be making some sort of protest over winter unless they have a very high income.