Sunak said the government wants to make sure the increase in prices is smaller initially and spread out over a longer period.
"We will spread out the price shock of rising energy bills over time," Sunak told the Commons.
People in council tax bands A to D will also get a £150 council tax rebate in April, Sunak confirmed, meaning 80 per cent of council taxpayers in England get the saving.
There will also be £150m for local authorities in England to help lower income households.
What's the reaction been?
Responding to Sunak in the Commons, Labour's shadow chancellor Rachel Reeves criticised him for not scrapping VAT on energy bills.
She said the "uncomfortable truth" is that families in Britain will still be paying hundreds of pounds more for energy, and cutting back to pay bills.
Reeves said the grants to power companies is a "buy now pay later scheme that loads up costs for tomorrow".
Labour MP for Rhondda Chris Bryant said £350 "isn’t going to touch the sides of the problem for my constituents".
He listed how costs have risen: gas and electricity up by £686, fuel rising by £314, the average weekly shop up by £385 over the course of a year, Universal Credit cut by £1,040, National Insurance up by £150 and frozen tax allowances costing £300.
It's a total of £2,875 a year in additional costs in a place where the average salary is £27,000, he said. But Sunak said Labour's proposals on energy would have saved less than his plans.