Bill Bullen, chief executive of Utilita – which serves prepayment meter customers – said government financial support was not directed sufficiently to those who needed it most.
He said ministers should spend money on “insulating the hell out of Britain”.
There are growing calls for help on bills ahead of the Spring Statement.
On Wednesday, Chancellor Rishi Sunak will deliver the statement – an update on the state of the UK economy, and an opportunity to outline further policies on tackling the rising cost of living.
The government is also preparing a UK energy strategy in light of the war in Ukraine and the impact it is having on global supply and prices.
Millions of households are facing a 54% rise in the cost of a typical annual gas and electricity bill, to about £2,000, when the regulator’s new, higher price cap takes effect on 1 April.
The price rise for prepayment meter customers, who can include some of the poorest and most vulnerable in society, is slightly higher. The increase for prepayment meter customers is typically £708 a year.
The war in Ukraine has heightened concern about a similar increase in October, when the next cap is set.
The government has said it is taking “decisive action” in helping people with their bills. This includes a £150 council tax rebate for 80% of households, followed by a £200 discount on bills in October which will need to be repaid.
However, Mr Bullen argued that the rise was inadequately focussed, leaving millions of people facing tough choices on their family budgets.
“They just do not have the money,” he said.
He said that the “path of no regret” for the government was to find ways to cut energy consumption, and therefore bills, over the long term with a massive home insulation programme. It was relatively easy, he said, to cut consumption by 20%.
Donate the rebate
Some people who agree with the criticism of a non-targeted approach to the government’s financial assistance have chosen to donate their £150 council rebate to charities helping those struggling to pay their fuel bills.
National Energy Action, which campaigns for warm, dry homes and runs a helpline and hardship funds, said that 40% of its donations in February came from people wishing to donate their rebate.