For the benefit of all of us who have to pay energy bills and taxes, I would suggest that it would be less costly and more effective to set AND ENFORCE  a realistic energy price cap at a level that in itself limits the amount of profits that energy companies are able to make

That would automatically...
1. Lower the bills that people are having to pay for energy
2. Eliminate or certainly reduce the current process of paying households a supplement to help them deal with the rising cost of energy.
3. Reduce the amount of additional taxation that will at some stage be required from people to support the current government spending in "handouts"
4. Reduce or eliminate the seemingly endless debates on how or whether to institute a "windfall tax" on energy companies profiting from the current crisis ... and, ultimately, the need for all the additional cost and manhours involved in trying to enforce any "windfall tax". 

In other words rather than try to chase companies and to get money back AFTER they've taken it (and had a chance to "squirrel it away" in their usual creative fashion), stop them getting it in the first place.

We need to break this toxic cycle where excessive pricing leads to higher profit for energy companies at the expense of higher prices for consumers and the need for government to step in to provide additional support which will ultimately have to be paid for by additional taxation on consumers who are already suffering because of higher energy prices.

As a rider to that, I would suggest that, as fuel companies appear to be likewise accumulating obscene profits from the general public at this time,  the implementation of an enforced "price cap" on petrol and diesel might serve a similar function.