When the UK’s new prime minister forms a government on September 6, he or she will need a rapid plan to address soaring household energy bills this winter.

With estimates that the annual average combined gas and electricity bill will rise from £1,971 in the summer to £3,582 at the start of October, and more than £4,000 by January, households are frightened that they will need to choose between heating and eating this winter.

Sir Keir Starmer, the Labour leader, declared the situation was a “national emergency” on Monday, echoing the consumer champion and founder of MoneySavingExpert.com, Martin Lewis, who said last week that households faced “a national crisis on the scale that we saw in the pandemic”.

Some 28.9mn households are connected to Great Britain’s electricity grid and these households are set to pay £59bn more for their energy over the next year, according to estimates from Cornwall Insight. That increase represents almost 2.5 per cent of the UK’s gross domestic product.

What are the main proposals to offer relief to households?

On Monday, Labour turned up the heat on Conservative party leadership candidates Liz Truss and Rishi Sunak with a promise that it would cap household energy bills at the current level of £1,971 over the winter if it was in power.

Its proposals to remove the threat of higher bills were more radical than suggestions from the energy industry for the government to remove some charges on bills unrelated to the wholesale cost of gas and pay for it from general taxation. This would take £420 a year off the current average bill, but would not prevent subsequent increases to reflect the much higher wholesale market price of gas and electricity.

The government has so far offered a £400 rebate for all households and an additional £650 for those receiving means-tested benefits, such as universal credit or pension credit. Pensioners will also get additional winter fuel payments as part of a £15bn package Sunak announced in May. The Institute for Fiscal Studies has estimated that to maintain the generosity of the support, an extra £12bn would be required.

The two leadership candidates have offered radically different ideas on what to do next. Sunak has promised to eliminate the 5 per cent value added tax on energy bills and offer £10bn additional support for vulnerable households.

Truss has been sceptical of offering what she called “handouts”, and has instead promised to cut taxes as well as some green levies from energy bills. However her team have not ruled out further direct support after intense criticism from Sunak.

How does Labour plan to pay for its proposals?

Starmer says his plan to cap bills at £1,971 this winter would cost £29bn, half the estimated annual increase in bills this year. Because households use more gas in winter than summer this will be an underestimate.

Labour proposes to make the government’s windfall tax retrospective from January rather than from May 26, the date Sunak announced it, leaving energy companies to fund £8bn of the cost at the expense of a more arbitrary tax system. The party would also reverse some of the support Sunak has announced, removing £484 for each household promised over the winter.

Finally, Labour said that by capping bills, inflation would be limited, peaking at around the current rate of 9 per cent rather than going up to 13 per cent, as the Bank of England forecast. This would save the government £7bn in the costs of servicing index-linked debt

According to Paul Johnson, director of the IFS, Labour’s proposals would be “very expensive” because he doubted they could be limited to just six months. “We’re looking at the cost of furlough”, he added.

Could energy support lower inflation and its cost to government?

Among advanced economies, the UK has an unusually high outstanding amount of government debt linked to the retail prices index of inflation. At the end of last week, some £547bn of index-linked debt existed, a quarter of total government debt.

This means that for every percentage point that RPI inflation rises in any one year, the cost of servicing index-linked government debt rises by £5.5bn. Although the Treasury does not have to physically pay the money until the debt is redeemed, it is included in public borrowing figures because the liability is generated in the year inflation was recorded.

Labour’s — and to a lesser extent, the energy companies’ — plan would provide a permanent saving if energy bills were only temporarily high, but six months of support would do little for the cost of government financing if it merely delayed a rise in prices.

More broadly, the government is hoping that the Office for National Statistics will classify its £400 support for households as a discount on bills when it pronounces its view on the issue on August 31. If the ONS says the help is akin to a discount, it would reduce peak inflation this winter by around 2 percentage points, according to FT calculations.

But most experts, including government officials, think the statistical agency will not oblige. The ONS needs to take a decision on the “economic reality” of the £400 discounts. If it decides this is really energy bills getting cheaper, inflation will be correspondingly lower. But if it decides that the government is simply giving households money regardless of the size of their bills, the support will be deemed akin to a universal welfare payment, and inflation will be unaffected.

What do economists recommend governments should do?

The IMF issued what should be seen as orthodox economic advice on soaring costs last month, saying that countries should offer targeted lump-sum support for vulnerable households, while letting energy prices reflect market forces.

This, it said, would protect poorer households while preserving the incentive to conserve energy as prices rose. It found many European countries were taking Labour’s approach and suppressing price rises, which it criticised for “keep[ing] global energy demand and prices higher than they would otherwise be”.

But with governments across Europe facing similar pressures, the UK would be far from alone if it simply fixed prices and absorbed the cost increases this winter like its continental counterparts.