As the opposition leader, Ed Miliband, mocked the prime minister in the wake of Major's call for state intervention on energy prices, Cameron announced an annual competition review to examine the cost of green regulations and the level of profits.
The PM said: "I can tell the house today that we will be having a proper competition test carried out over the next year to get to the bottom of whether this market can be more competitive. I want more companies, I want better regulation, I want better deal for consumers. But yes we also need to roll back the green charges that he put in place as energy secretary."
The review, which will be carried out by the Office of Fair Trading and the new Competition and Markets Authority, is to be announced next week in the annual energy statement. George Osborne is to announce any changes to levies in his autumn statement.
Downing Street later said the prime minister was determined to roll back the costs of green levies. But government figures showed that the largest proportion of the £112 the charges add to the average bill are aimed specifically at less affluent people.
This may place Cameron on a further collision course with Major, who said in his speech on Tuesday that the government needed to make sure that less well off people do not face a choice between deciding whether to pay for heating or eating.
The government figures show that £50 goes on the energy company obligation – which supports energy efficiency in poorer households. A further £11 goes towards the warm homes discount, which is designed to help with the costs of fuel bills for poorer households.
The other charges are meeting the UK's renewable obligations (£30), the EU's emissions trading scheme (£8), the carbon price floor (£5), feed-in tariffs (£7) and smart meters (£3). These come to £114, slightly more than the £112 identified by the prime minister. Labour pointed out that £67 of the £112 was introduced by the coalition.
The PM announced the review as Miliband said that Major's call for a windfall on the profits of energy companies showed that No 10 has misjudged the mood of the nation by appearing to rule out state intervention.
Cameron dismissed Miliband as a "con man" after pledging to introduce a 20-month price freeze if he wins the election, prompting a rebuke from the Commons Speaker, John Bercow, for using unparliamentary language.
But Cameron showed that Major had hit a nerve when he announced the review of the level of profits and the impact of the cost of green regulations.
He said: "We need to recognise there are four bits to an energy bill. There are the wholesale prices, which are beyond our control. There are the costs of transmission and the grid, which are difficult to change. There are the profits of the energy companies and there are the green regulations. It is those last two that we need to get to grips with."
The PM told the rightwing backbencher Brian Binley that he was targeting £112 on bills.
"We have to have an honest discussion about this. On our energy bills is £112 of green taxes and green regulations. We need to work out what is necessary to encourage renewable energy, what is necessary to go on winning overseas investment into the UK but how we can bear down on people's bills.
"It simply is the politics of the con man to pretend that you can freeze prices when you are not in control of global energy prices. The proper approach is to look at what is driving up bills and deal with it."
Miliband mocked the PM for inconsistency. "He really is changing his policy every day of the week. It is absolutely extraordinary. His energy secretary [the Liberal Democrat Ed Davey], who is in his place, says it has nothing to do with green taxes, 60% of the green taxes were introduced by him. And who is the man who said vote blue to go green? It was him. I tell you what's weak - it's not standing up to the energy companies, and that is this prime minister all over."
Miliband opened by saying that it was difficult for Cameron to dismiss his call for state intervention after Major's call for a windfall tax. The Labour leader said: "The prime minister said that anyone who wanted to intervene in energy markets was living in a Marxist universe. Can he tell the house how does he feel now that the red peril has claimed Sir John Major?"
Bercow interrupted the proceedings to criticise the prime minister for describing Miliband as a con man. He said: "Let me just say. I let it go the first time … 'con man' is frankly unparliamentary. The prime minister is a man of great versatility in the use of language. It is a bit below the level. We'll leave it at that."
The PM's spokesman denied claims of a coalition rift because ministers agreed on the need to tackle the cost of living.
The spokesman said: "One way or the other the prime minister is determined to roll back green levies. There have been discussions about more targeted support since George Osborne's speech on 9 September."
A Labour spokesman said: "The prime minister is clearly on the defensive over energy prices. He is refusing to take real action to tackle overcharging now. He wants to take over a year to come up with proposals at a time when bills are going up 10%."
A senior Liberal Democrat source responded to the Cameron announcement: "Everybody knows the Tories are getting cold feet on the environment. The Tories have put no properly worked up policies in front of us.
"But we will not allow a panicky U-turn during PMQs to dictate government policy. The way to provide stable fuel bills now and in the future is not to make policy up on the hoof. Liberal Democrats in government will not allow the Tories to undermine our commitment to the environment, hurt the fuel poor or destroy our renewable energy industry.
"Nick Clegg has always said that we should stress-test every policy to make sure that there isn't a penny more on bills than necessary. Of course, we will look at the specific details of what the Tories propose. That is coalition government.
"We will discuss the means but we are not prepared to compromise on the ends – protecting the environment, helping the fuel poor and safeguarding our green industries and jobs."
A reduction in what the prime minister's calls "green charges" from energy bills may mean that the shortfall will have to be met from general taxation. Nicola Sturgeon, the Scottish deputy first minister, has pledged to cut energy bills by 5% (around £70) if the SNP is elected to govern an independent Scotland. The SNP would achieve this by funding green levies through general taxation.