The energy secretary, Ed Davey, called on electricity and gas suppliers to act rapidly to reveal their true profitability to customers and the energy regulator, as the government spent another day on the defensive over soaring bills.

Davey's aides urged Ofgem to complete a review of the industry's profitability and explain how it managed to produce its estimates of the cost of government green levies.

He said: "We need more transparency from the big six." He argued that companies such as Centrica, which owns British Gas, "need to be held to account for the profits they make and they need to declare them in a much clearer way".

Davey has singled out British Gas, saying his department estimates that ECO – the energy company obligation, money used to help insulate homes – makes up £47 of the average annual energy bill.

But when British Gas announced a 10% price increase on Thursday, it put £40 of that rise down to ECO, a calculation not accepted by the Department of Energy & Climate Change.

On Monday, ministers will hope to move the debate away from energy prices. Davey will announce the crucial contract that paves the way for the first nuclear power plant to be built in a generation, by unveiling the "strike price" at which a consortium led by France's EDF will be able to sell the electricity generated at the new Hinkley Point to the national grid.

Sources say the two sides are inching close to an agreement based on a figure of about £90–£92 per megawatt hour – a floor that would be almost twice the present wholesale price of electricity. The new nuclear energy programme is at least five years behind schedule and the new Hinkley plant will not be feeding into the grid until 2020.

In a sign of how toxic the issue of energy bills is becoming for the Cameron government, the Scottish National party, at its last conference before the referendum on independence, promised cheaper energy bills if Scotland votes to break away.

The SNP deputy leader, Nicola Sturgeon, said an independent Scottish government would cut energy bills by 5%, remove levies for tackling fuel poverty and improving energy efficiency from people's bills, and instead fund the scheme directly.

The money an independent Scotland would receive from the European Union's emission trading scheme would at least partly cover the cost of it, according to the SNP. The party clearly hopes the promise could be a game-changer in the debate over independence in the same way that a similar promise by the Labour leader, Ed Miliband, appears to have had resonance on the English political stage.

Coalition ministers freely admit they do not even know if, or by how much, the remaining energy companies such as EDF are likely to raise bills this winter. Only two – SSE and British Gas – have so far announced winter price rises, leaving Downing Street braced for further waves of bad news in the weeks ahead.

The energy firms have no legal duty to inform the government in advance, although in practice Davey has so far been given overnight market-sensitive warnings. One source at the Department of Energy likened it politically to waiting week after week for bank bonus figures.

But despite the prevailing environment, No 10, following a political agreement across the coalition, has decided not to try to match Miliband's call for a 20-month price freeze. That decision leaves ministers only able to urge customers to shop around for cheaper prices.

In a sign of the sensitivity of energy prices, Downing Street was reluctantly drawn into a row over whether people should wear jumpers to reduce their energy bills. The prime minister's spokesman said it was something people should consider if charities advised it was a good move, a day after Davey told Newsnight he wore jumpers at home to keep bills down.

But No 10 later had to backtrack, saying: "The prime minister would point people to a range of things being done to help people with their fuel bills, such as legislating to put everyone on the best tariff for them. He believes Labour's 'price-freeze' policy is a con, and certainly would not advise people on what they should wear."

Miliband nevertheless seized on the remarks, saying: "Their crime policy used to be: hug a hoodie. Now their energy policy appears to be: wear a hoodie. Never let the government tell you that there's nothing they can do, or that it's your responsibility to sort out the problems in our energy market."