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The cost to the government of shielding households from soaring energy bills is expected to double in the new year to up to £5bn a month after a hike in Ofgem’s price cap.

The energy regulator said on Thursday that its price cap will reach the equivalent of £4,279 a year for the average household from January.

Ofgem said the cap, which is adjusted every quarter, will increase by £730 for the three months from the start of next year. However, the government’s energy price guarantee (EPG) limits the typical annual bill in Great Britain to £2,500 in the same period.

Although the importance of the Ofgem price cap for households is reduced by the EPG, it still matters because the cost of the Treasury subsidy on bills is linked to the difference between the two.

The government provides energy suppliers with the difference between the unit rate under the EPG, and what they would have charged their customers were it not in place, a rate set by the Ofgem cap.

The new cap will force the Treasury to pay 33p per unit of electricity and nearly 7p per unit of gas that households use. Energy consultancy Auxilione said this will push up the cost of running the EPG from £7.8bn in the last three months of 2022 to £15.1bn in the first three months of next year.

The energy supplier Ovo estimates the government will pay around 33p every time someone uses their oven for half an hour or an electric shower for six minutes.

The chancellor, Jeremy Hunt, said in last week’s autumn statement that the EPG will be lifted to £3,000 for a typical household from April, which should reduce the amount the Treasury must pay in subsidy.

Average household bills were limited to £1,277 a year ago, under Ofgem’s price cap. That had been due to rise to £3,549 from October.

However, the former prime minister Liz Truss intervened to introduce the EPG for two years. Hunt later truncated this to six months, before then extending it by 12 months from April.

The consultancy Cornwall Insight has predicted the EPG will cost the government £42bn in its entirety, representing about £2.3bn a month. Investec estimates the policy will cost £24bn, or an average of £4bn a month, for the first six months.

Forecasts of the cost of the EPG are highly dependent on the wholesale price of gas, which has been volatile, particularly since Russia’s invasion of Ukraine.

Ofgem has changed the frequency of changes to the cap from every six months to quarterly to respond more quickly to movements in energy markets. Cornwall Insight expects the cap to reduce to £3,921 from April and then to about £3,400 for the last six months of 2023.

The Treasury said last week that £1.8bn was paid out in October through the energy bills support scheme, reducing costs for more than 27m households. It said £136m worth of vouchers had been provided to traditional prepayment meter customers.

The government hopes to fund some of the cost of the scheme through windfall taxes on oil and gas and electricity generation companies. The mild start to winter, and an easing in the price of wholesale gas, will have helped reduce the cost of the policy to the taxpayer.

However, there are concerns that bills will remain high next year as countries struggle to replace supplies of Russian gas, which have been cut since the invasion of Ukraine.

The Department for Business, Energy and Industrial Strategy said: “The energy price guarantee is protecting consumers from soaring energy costs, meaning people’s bills will not rise in line with today’s Ofgem energy price cap increase.”

Separately, ministers are planning to launch a £25m public information campaign before Christmas to encourage people to save money and energy.

The campaign will advise eight changes to cut bills including reducing the temperature of boilers, turning off radiators in empty rooms and switching off electrical devices rather than leaving them on standby, The Times reported. The measures could save households up to £420 a year.

Truss had blocked a public information campaign, arguing it could be seen as “nannying” Britons.