Consumers will have to cope with extraordinarily high fuel bills for at least another 18 months, the boss of Britain’s biggest energy supplier has said.

Michael Lewis, the chief executive of E.ON UK, called for “very substantial” government intervention to help people with escalating fuel bills, one of the biggest factors in the cost-of-living crisis.

Bills could reach £3,000 when the price cap lifts in October, he said, when people would also need more gas and electricity to heat their homes.

Lewis said E.ON expected almost one in five customers to struggle to pay their bills in the autumn, when price rises were “baked in”. He said 1m of E.ON’s 8m accounts were already in arrears and the firm forecast a 50% rise in October.

About 40% of people were likely to be in fuel poverty, meaning more than 10% of their disposable income would be needed to pay fuel bills, he said.

Speaking on the BBC Sunday Morning show, Lewis said: “I read emails from customers regularly, I listen in on calls, and frankly, some people are at the edge. They simply cannot pay and that will get worse.”

He said the huge increase in the cost of gas, which also drove up the price of electricity generation, was predominantly down to the Russian invasion of Ukraine. The price cap for consumer bills had a record rise last month from £1,277 to £1,971 a year and is expected to rise to at least £2,600 in October.

Lewis said: “It’s a very, very significant impact and that’s why we’ve called upon the government to take more action. We do need more intervention in October and it has to be very substantial.”

Double the number of households should be given the warm homes discount, and the rebate should go up from £140 to £600, he suggested, urging the government to “tax those with the broadest shoulders”.

He said: “I think for the next 18 months we’re likely to see higher prices. That’s already baked in, certainly in October and probably into next year as well. I think the longer-term development depends on what happens in the war in Ukraine [and] how Russian gas flows will develop.”

The E.ON boss said the drive to net zero was “the long-term way to get off gas, to get off international gas prices and to drive down costs over the long term”.

Labour renewed its calls for a windfall tax on North Sea oil and gas producers. Rachel Reeves, the shadow chancellor, said Lewis’s comments “underline how tough the cost-of-living crisis is for families, and how Conservative delays will see the situation get even worse.

“The government must act now, by bringing in a windfall tax on oil and gas producer profits to cut bills.”

Ministers said that they would consider such a tax among other options, although many have played down the idea. Asked directly about a windfall tax on Sunday, Nadhim Zahawi, the education secretary, told Sky News: “We will look at all the options.”