The coalition has unveiled measures it says will knock £50 off the average energy bill, but some of that cost will be absorbed by taxpayers.
The Government has laid out its ideas on how to cut energy bills this winter - but the plan has been put together in haste.
The so-called big six energy companies were forced to explain to Parliament why bills are increasing so much this winter.
The Co-operative Energy firm has announced a price rise of 2.5% on average.
In an email to customers, the company said: "As winter sets in and some energy companies raise their prices by as much as 10%, we’ve got some good news for you to warm to.
"Co-operative Energy is raising its prices on 8 January…but only by 2.5% on average across all our customers."
Energy Secretary Edward Davey called E.ON's price rises announcement "disappointing news".
Bur Mr Davey stressed:
This rise is ... lower than it would have been as a result of Government action to reduce the impact of price rises on consumers.
As part of their announcement today, E.ON have confirmed they will pass on these savings to their customers.
This does not let energy companies off the hook.
Asked about the timing of E.ON's price rises announcement, which came amid media focus on the death of Nelson Mandela and the devastating storms across the UK, Downing Street said, "It is for them to explain their decisions."
E.ON has announced its customers' dual fuel energy bills will increase by an average of 3.7% from January 18.
The company said that means the average variable dual fuel bill will go up by £48, electricity only prices will increase by 3.7% or £20, and gas only bills will climb by 4.6% or £37.
Chief executive Tony Cocker said changes announced by the Government earlier this week reduced the overall level of the rise that was necessary to cover extra costs.
The energy firm said it was "working hard to limit the impact on its customers" by announcing a lower average percentage rise than any other major supplier.
Earlier this week, E.ON said it did not expect to have to raise prices in the next 18 months "as a result of social or environment obligations".
But E.ON also warned, "There remains a risk, however, that increases in network charges or wholesale energy costs for example could force a price increase".
The announcement followed the Government's shake-up of green levies on Monday.
Energy supplier E.ON will increase prices by an average of 3.7% from January 18.
Prime Minister David Cameron has told ITV News' Deputy Political Editor Chris Ship that the coalition's announced cut in energy bills was not in response to Labour's proposed energy price freeze.
Speaking in China, Mr Cameron said: "We have been discussing within the coalition the issue of energy bills for years now. It has taken me longer than I would have liked but I'm very glad we put in place at least some relief on the issue of energy bills."
The boss of energy firm npower has said he would be receiving a "much reduced" bonus because of his company's poor customer service.
Chief executive Paul Massara apologised for what regulator Ofgem dubbed the "serious deterioration" in customer service.
He told Daybreak: "The fact is we haven't delivered the customer service they deserve.
"When the board sit down and review my bonus they will reduce my bonus because I haven't actually delivered for customers."
Energy companies were guilty of "outrageous blackmail", according to a consumer campaigner, who saw the latest attempt to cut bills by £50 as an empty gesture.
"I'd be more impressed if energy companies had said they were going to lower bills by an average of £50 and were going to do it now," Ann Robinson of Uswitch told Daybreak.
She expressed scepticism over the "Big Six" energy companies motivation and what the Government could do to intervene on behalf of struggling consumers:
"I think there is a limit to what can be done. It is playing around the edges. It is not real. I also hear for example, is that one of things that the energy company is looking to is to delay even more the smart meter programme."
npower received five times as many complaints as the best performing energy firm SSE, research showed.
- npower had 202.5 complaints per 100,000, compared with 38.3 for SSE - the lowest level of the main energy providers - from the April to June period, Consumer Futures research showed.
npower also recently announced a 10% average bill increase but has said that it will reduce bills as a result of a shake-up of Government green levies.