The government is to scrap a plan to give people £200 off bills from October which would be repaid over five years.
Instead, the BBC understands that sum will be increased and possibly doubled, and will not need to be paid back.
One-off payments to some vulnerable households and another cut in VAT on fuel could also be announced.
The support, to be announced by Chancellor Rishi Sunak later, is expected to be largely funded by a windfall tax on oil and gas firms that could raise £7bn.
It comes a day after Sue Gray’s critical report into lockdown parties in Downing Street and follows intense pressure on the government to do more to help people with the cost of living crisis.
Labour has repeatedly called for a windfall tax on energy companies that have made bumper profits, in large part because of Russia’s invasion of Ukraine.
But until now the government had resisted calls to impose the one-off levy, with some senior members of the cabinet arguing it could deter energy firms from investing in the UK.
However, it is understood the prime minister has now sided with Mr Sunak who had been pushing for the tax.
But proposals to tax income from other electricity producers, such as some older windfarms and nuclear plants which have also seen windfall gains, have been shelved.
And companies that increase investment in the UK could earn a discount on the additional tax.
The Treasury said the government understood “that people are struggling with rising prices” and that Mr Sunak had been “clear that as the situation evolves, so will our response”.
The announcement of more support comes after the UK’s energy regulator Ofgem warned this week that the typical household energy bill was set to rise by £800 in October, bringing the typical household bill to £2,800 a year. Bills had already risen on average by £700 in April.
Ofgem warned it meant 12 million households could be placed into fuel poverty.
Most people living in homes in England in council tax bands A-D have already received a £150 rebate on their bills.
Paul Johnson, director of the Institute for Fiscal Studies, said it was important most of the government support was targeted at those on the lowest incomes.
He told the BBC offering a universal payment would mean a lot of the money would go to households who “don’t desperately need it”.
He also warned putting billions of pounds into the economy at a time when prices were rising quickly “could stoke additional demand and make the inflation much more permanent”.
Impact of war in Ukraine
Energy firms have made huge profits following Russia’s invasion of Ukraine.
Shell reported a record £7bn profit in the first three months of this year while BP made £5bn, the highest for 10 years.
But Offshore Energies UK, which represents the offshore oil and gas industry, said a windfall tax on energy firms would see higher prices and do long-term damage to the oil and gas industry.
Deirdre Michie, chief executive of the body, said: “This is an industry that thinks and plans long-term, so sudden new costs, like this proposed tax, will disrupt planning and investment and, above all, undermine investor confidence.”
Higher energy bills are pushing prices to rise at the fastest rate for 40 years, with fuel and food costs also biting into household budgets.
Ofgem chief executive Jonathan Brearley said conditions in the global gas market had worsened after Russia’s invasion and warned that the price cap could rise beyond £2,800 if Moscow decided to disrupt supplies.
Europe gets about 40% of its natural gas from Russia, so sudden supply cuts could have a huge economic impact.
While the UK would not be directly impacted by supply disruption – as it imports less than 5% of its gas from Russia – it would be affected by prices rising on global markets as demand in Europe increased.
Mr Brearley told MPs price rises in the gas market were “a once-in-a-generation event not seen since the oil crisis of the 1970s”.