Domestic energy prices are forecast to rise by 5% from April, adding £85 a year to household bills, according to consultancy Cornwall Insight.
The forecaster, which is widely regarded for its accurate predictions, said a household using a typical amount of gas and electricity would pay £1,823 a year.
The figures emerged as Energy Secretary Ed Miliband wrote an urgent letter to Ofgem, the regulator which sets the price cap, asking it to move quickly to protect consumers.
The predicted higher prices will take effect at the same time as increases to water and council tax bills in April.
However, minimum wage levels will also go up while benefits and the state pension will increase.
Cornwall forecasts that the price cap will rise from its current level of £1,738 per year for a typical household.
Higher household bills are likely to add pressure to the government who are already facing criticism for removing the winter fuel allowance from elderly people not claiming the pension credit or other means-tested financial support.
Ofgem will announce the official new energy price cap level on 25 February, which will affect homes in England, Wales and Scotland.
The predicted rise will come as the days get lighter and warmer, when energy use tends to fall.
Cornwall say the hike is due to a combination of colder weather and a fall in gas storage levels across Europe, which has led to a sharp rise in wholesale prices.
Bills are about 50% higher than pre-Covid levels, but remain below the peak reached in 2022 when Russia’s full-scale invasion of Ukraine caused energy prices to spike.
The price cap affects 26 million households on default, variable tariffs and is set every three months by Ofgem.
While the cost of each unit of gas and electricity is capped, the total bill is not, so household bills will vary depending on how much energy is used.
The regulator illustrates the cap by showing the impact on the annual bill of a household with typical energy usage.
In January, there was a 1.2% rise – which worked out as £1.75 extra a month compared with the previous cap.
A period of high prices means households have collectively built up debt of £3.8bn to suppliers.
The average household in arrears owes more than £1,500 for electricity and £1,300 for gas.
A rise in the energy cap would mean a third successive increase in energy bills at a time of year when the weather starts to get warmer and households would usually hope to see a reprieve in costs.
National Energy Action (NEA), a charity aimed at helping people struggling with energy bills, said it will feel like an “interminable winter” for many.
“There is no getting used to this new normal for the people we try to help,” said NEA’s chief executive Adam Scorer.
“Millions of the most vulnerable households are struggling with debt and severely rationing their heating.”
The Energy Savings Trust said changes to how buildings are insulated helps to lower bills.
The trust’s head of policy, Stew Horne, said: “We’re urging policymakers to put in place clear, actionable steps to help people upgrade their homes to make them warmer and more affordable to heat.”
He suggested setting up a national retrofit advice service to “enable people to feel confident to install measures, such as insulation and draught proofing”.
In his letter to the regulator, Miliband asked the Ofgem chief executive to set out faster means it can pursue to ease the pressure of the “rollercoaster” of global gas markets.
“In recent months we have seen once again the dangers for our country of being exposed to fossil fuel markets controlled by petrostates and dictators,” he wrote.
“Once again, the British people and British businesses will face the consequences of fossil fuel markets we do not control,” he added.
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