The collateral damage in the great energy debate is mounting by the day. As the party leaders scrabble to come up with something to say in response to public concern about bills, the costs so far include their reputations for sound economics, the investment plans of many businesses and, potentially, the transition to a low-carbon future. Never mind the grandchildren's planet: burn, baby, burn.

As bills go up between 8.2% (SSE) and 10.4% (npower), there is no doubt about the pain. The average bill is £1,267. This hits household budgets hard and has been a significant factor undermining consumers' confidence about spending.

The blame game has begun. Labour blames the energy companies, and wants a freeze. John Major implicitly agrees by proposing a windfall tax on their profits. The Tory right blames onshore wind, ironically the cheapest of renewables. The energy companies blame green taxes, and want them cut.

The prime minister, once long ago pictured hugging a husky in the Arctic, duly panics despite the risk to his integrity and image. He promises to cut green taxes even though his own Tory manifesto pledged: "We will increase the proportion of tax revenues accounted for by environmental taxes."

Is anyone right in the blame game? Let's start with the companies. Like most businesses, they are not above some jiggery-pokery with estimated bills, some fancy tax-dodging, and the selective presentation of the facts. They have repeatedly run scare stories about the cost of the regulatory requirements imposed on them.

Energy UK, their lobbying body, claimed last year that the eco subsidy (which helps the fuel-poor and those living in leaky old houses) would cost £1.7bn to £2.35bn. In fact there is a trade in the insulating projects that the companies have to undertake. Those who do too many can sell to those who have fallen short, and that market shows that the true cost is exactly what the government planned, at £1.3bn a year.

There is a difference, though, between playing grandmother's footsteps with the regulator, self-serving lobbying, and the more significant charge that they rig the market. The market has been inspected repeatedly, most recently by Ofgem in its retail market review. The charge does not stick. Gas prices are the lowest in western Europe, and electricity prices the third lowest. Nor do prices go up more quickly than down.

Far from being bullying behemoths, the energy giants are looking like threatened dinosaurs. The profits of all six are rising with recovery, but last year they totalled £3.74bn, which is a little more than half the profits of just one bank, Barclays. Their way of making money – selling more energy from big power stations – is under global attack.

Those low-energy light bulbs are working, so electricity demand is still below its peaks in Europe. The trend for householders to produce their own electricity is hitting the giants hard, as are renewables. When the wind blows and the sun shines, electricity can flood on to national grids. In Germany the wholesale electricity price has on occasion gone negative, which is a power company's nightmare if you are trying to make a return on big coal, gas or nuclear to pay to your pension-fund shareholders.

Nor are green taxes to blame. They are too small. About 9% of energy bills are government charges. Some 5% go on the eco subsidy. Without these policies, bills would be more painful for the most vulnerable, and higher for many others.

About 4% goes to support low-carbon electricity from renewables. These policies decarbonise the electricity sector, tackling climate change. They also give us energy security, and protect the consumer against volatile fossil fuel prices.

Overall, the government's policies – backed until recently by three-party consensus – are forecast by Whitehall economists to cut energy bills, not increase them. They will save consumers about £166 a year (or 11%) by 2020 thanks to energy saving and diversification from fossil fuels.

The only easy green tax to ditch is the carbon price floor, an unnecessary charge on electricity generated from oil, coal and gas. It is not needed to decarbonise electricity but it collects £600m this year, adding £5 to bills. It will steadily rise to add more than £20. The Liberal Democrats did not want it, but George Osborne insisted on the revenue.

It is possible, of course, that some programmes now funded from energy bills could be paid from taxation, but ministers will find that they cannot ditch these policies. First, it would be foolish to raise future energy bills by slowing energy-saving and the shift to renewables.

Second, there is a legislated fuel poverty target, and ministers would find themselves fighting a judicial review. The same applies to renewables, as we agreed an EU legal target of 15% of our energy from renewables by 2020.

The real blame for high bills is our excessive reliance on gas and coal, and the world market price. Not even the British prime minister has much power over that.

Sadly, few people these days read Cervantes. David Cameron should. He looks increasingly like Don Quixote, tilting at windmills.