Consider the benefits of giving Ofgem powers to set a Variable Price cap on energy tariffs, based on a 'volume pricing' model, with different rates depending on a household's council tax band.
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For example:
Those living in council tax band F, could be charged 5p per kWh per month for the first 500 kwh, increasing to 7p per kWh per month, for the next 250 kwh, increasing to 9p per kWh per month for the next 250 kwh..... etc
Those living in council tax band H, could be charged 9p per kWh per month for the first 500 kwh, increasing to 12p per kWh per month, for the next 250 kwh, increasing to 15p per kWh per month for the next 250 kwh..... etc
This method of pricing would reward those who use less energy, encouraging people to reduce consumption, and it allows those whose assets indicate they may be able to afford more, to subsidise those whose assets indicate they may struggle.