Ministers’ crunch talks with energy bosses have failed to deliver a breakthrough despite the industry’s calls for an urgent intervention and a warning from the founder of Ovo Energy that household bills will “almost certainly” double in April.

The business secretary, Kwasi Kwarteng, held the virtual meeting on Monday to address fears that the winter energy crisis may escalate after new gas price highs across Europe last week.

Kwarteng is understood to have met individually with energy bosses from the UK’s largest energy suppliers about twice each in the week running up to Christmas, when new record energy market highs reignited fears that industry costs could spiral and that more energy suppliers could go bust in the months ahead.

Related: Rising energy prices will give Treasury £3.1bn windfall, says Labour

However, the joint meeting ended without resolution, with talks over the industry rescue plans drawn up by the regulator expected to continue in the weeks ahead, despite growing calls for urgent action to protect households from the cost of the energy crisis.

Stephen Fitzpatrick, chief executive of energy supplier Ovo, told the BBC there had been “nowhere near enough urgency” from the government, even as soaring wholesale costs threatened “an enormous crisis for 2022”.

“From where they were April 2021 to April 2022 it looks almost certain now that bills are going to reach £2,000 per household, which is going to be double what they were paying last year,” he said.

A source told the Daily Telegraph that the UK faces a “doubling or trebling of bills”, with the government being called on to plug an estimated £20bn rise in the global cost of energy.

Gas prices surged last week to 450p a therm, about nine times higher than a year ago, surpassing the record high set in October this year as supplies from Russia slowed despite rising demand to beat the winter cold.

“We’ve seen this energy crisis unfold now for the last three months and we’ve watched as energy prices have spiked, fallen back and spiked again,” Fitzpatrick said.

“We’ve had more than 30 bankruptcies in the sector, we’ve had millions of customers forced to change supplier. The cost to the consumer has already been more than £4bn.”

He added: “We haven’t seen any action from the government or from the regulator. There’s an acceptance that there’s a problem, but nowhere near enough urgency to find a solution.”

A government spokesperson confirmed that a meeting was held between the business secretary, energy bosses and Ofgem to discuss “the ongoing effects of record high global gas prices on the sector”.

“Throughout the meeting there was discussion of the issues facing the sector and an agreement for meetings to continue over the coming days and weeks to ensure UK consumers are protected,” the spokesperson added.

Nigel Pocklington, the chief executive of supplier Good Energy, told investors last week that “no one in the industry is immune” to the surge in market prices, and called on the government to “support the industry at large in navigating these short-term challenges to protect bill-payers and those that serve them”.

“This is a national crisis,” Pocklington said. “Wholesale gas and power prices have increased to unprecedented levels over the last three weeks, creating an extremely difficult operating environment for every business in the industry.”

Energy bosses are expected to call for the government to offer help to hard-hit households by cutting VAT from bills, and moving green support levies into general taxation.

They are also expected to discuss new ways to manage the cost of energy company failures, which has affected millions of households since September.

The government also faces growing calls from opposition parties to take action against the energy crisis, which has caused the steepest ever winter bill hike in October and is likely to lead to even larger increases in April when the regulator is due to reset its energy price cap.

The Liberal Democrats have calculated that households are likely to pay a total of £100m more for their gas and electricity between Christmas and the new year compared with last year.

Ed Davey, the party’s leader, said the government had “totally failed to tackle the problem” and called on ministers to double the financial help offered through the warm home discount scheme.