Ministers are facing growing pressure to lower energy costs as households in Great Britain face the steepest rise in summer bills in four years this week.

The quarterly cap on gas and electricity charges will rise by 13% from Wednesday to the equivalent of £1,862 a year for an average household, just days after figures revealed that consumer energy debt had reached record highs.

Unpaid energy bills have climbed by £240m in the past three months, according to the data released by the industry regulator Ofgem, last week, to reach an all-time high of almost £4.8bn.

Andy Burnham, who appears set to become the next prime minister, will face immediate calls to tackle high energy bills upon taking power, amid fears over their impact this winter. The chancellor, Rachel Reeves, has previously ruled out offering the universal energy support provided by Liz Truss’s government in 2022.

James Mabey, a policy analyst at National Energy Action, a fuel poverty charity, said: “The consequences of energy debt include cold homes, rising anxiety and impossible choices about essentials. The right response is to scale debt relief.”

As households have fallen deeper into debt, wholesale energy prices have surged due to the war in Iran, which has disrupted oil and gas shipments via the strait of Hormuz for the past four months.

Until this week, the quarterly price cap has delayed the full impact of the crisis on household bills – but the surge in wholesale prices will be passed on from 1 July and remain elevated until the next price cap takes effect at the start of October.

Nigel Pocklington, the chief executive of the supplier Good Energy, said: “Rising energy bills are becoming a financial nightmare for millions of households across the UK, with many people unsure how they’re going to keep up with the current payments, let alone rising costs.

“We need to urgently reform the way the market operates to deliver and incentivise a cleaner, more affordable energy system. The priority now should be turning that into action.”

He added: “The next prime minister must set out a clear plan for how Britain will move away from high gas prices and bring bills down for good.

“The Labour government still has time to deliver on its ambition to cut household bills, but doing so requires urgent action to decouple electricity prices from gas, so consumers can fully benefit from lower-cost, homegrown clean energy.”

Good Energy has set out a proposal which, combined with recent government measures to reduce bills by £150 a year, could cut household costs by £270 annually – close to Labour’s manifesto pledge to cut £300 a year from home energy bills by 2030.

It has called on the government to move the cost of supporting government policies away from energy bills and into general taxation, while increasing payments through its warm home discount scheme by £300 – bringing them to £450 – for 6 million vulnerable households.

This would cost the Treasury about £10.1bn and save the typical bill payer £76 a year, while vulnerable households would save £376 a year, according to the company.

Good Energy has also joined calls for the government to move ahead with plans to break the link between expensive gas power and the overall electricity market price, by taking gas plants out of the market and into a strategic reserve. Under the plans, generators would be paid a steady fixed rate to run their gas plants only as a last resort.

The plan could save up to £60 a year for households and could be delivered within two years, according to separate analysis by Greenpeace and consultants at Stonehaven, which have also backed the creation of a gas plant reserve.

“It may not be the final answer,” Pocklington said, “but it demonstrates that credible steps can be taken now to break the link with gas and reduce bills, while keeping the need for longer-term reform firmly on the political agenda.”

A government spokesperson said: “We have taken £150 of costs off energy bills for the years ahead and extended the warm home discount to around 6 million households.

“We are going further and faster to move on to homegrown energy we control, including taking decisive action to break the influence of gas on electricity prices, to better protect households from energy crises.”