Denver Mckay is used to being cold. Heating his one-bedroom flat in Hamilton, just outside Glasgow, is a luxury he can’t always afford. “I pay £20 a week now and this is a struggle,” he said. “Sometimes I have to go without the heating on at all. Sometimes it’s just one room.”

He is worried about impending gas and electricity price rises. In the last month Scottish Power, Npower and E.ON have all raised their prices by about 8%, adding up to £100 a year to customers’ bills. Mckay’s supplier, EDF Energy, raised electricity prices in December but cut gas prices, amounting to a 1.2% overall increase.

“I can’t afford to pay any more, so I’ll just have to not switch it on as much,” he said. “I get £70 a week. I have to pay £30 extra to cover my rent. I can’t afford more than £20.”

Mckay moved from Cheshire three years ago after his marriage broke down, and although he has found some temporary jobs as a warehouse worker for Marks and Spencer he is currently unemployed.

To make his £70 a week go further, he switched suppliers from Scottish Power in September, but is still in dispute over a final bill for an extra £600.

“It was £500 for gas and £100 for electricity,” he said. “I don’t know why, but I checked it out and apparently they can do that. I was on the wrong tariff or something, even though I was pre-paying. But I can’t pay it – where am I going to get £600 from?”

Mckay’s problem is shared by about one in 10 households across the country who are classed as in fuel poverty. Ofgem, the energy regulator, is introducing a price cap on pre-payment customers from April, but the majority of people in fuel poverty have standard meters, and everyone will be affected by rising prices.

The stock answer that Ofgem, energy suppliers, price comparison websites and consumer champions give to complaints about rising fuel prices has been the same for a decade: switch.

Switching from “standard variable tariffs” – the default price plan – to the cheapest deal would save about £230, the regulator says.

Yet even though UK consumers have been able to choose suppliers since 2001, and price comparison websites like uSwitch.com, TheEnergyShop.com and moneysavingexpert.com have been in business for nearly a decade, only a third of us have bothered to switch.

That leaves 66% – 20 million households – who still pay more than they need to, the so-called “sticky” customers. About 45% of us don’t remember ever changing suppliers.

It is no wonder few people switch when switching remains complicated, according to Joe Malinowski, founder of TheEnergyShop.com. “One supplier asks you 28 questions just to get a quote. Why does it take three weeks to change suppliers when you can change mobile phones in a week or insurance even more quickly?”

Even those who do switch to a fixed-price deal have to stay alert. Once the fixed period has ended, unless they switch again they will be moved back on to a standard variable tariff.

So energy companies have little incentive to give the sticky 66% a good deal, which results in “excessive prices” generating about £2bn a year for the big six – British Gas, Scottish Power, EDF, SSE, Npower and E.ON – according to a landmark report by the Competition and Markets Authority last year.

“It’s privatisation that’s the problem,” Mckay said. “The government has given them billions, and their bosses are taking home million-pound salaries. It doesn’t matter if they’re rubbish. But what can you do?”

Mckay’s question is one that John Penrose and Caroline Flint are trying to answer. Penrose, a former cabinet office minister, and Flint, a former shadow energy secretary, have been leading a parliamentary fightback, assisted by the SNP’s Patricia Gibson.

They have secured a rare backbench debate on Thursday, backed by more than 50 MPs from all parties, calling for protection for the sticky 66%.

“I want nothing less than a protected tariff – a temporary price cap – for customers on standard variable tariffs, who are simply being ripped off year after year,” Flint said. “This cannot go on.”

She has been fighting for fair energy prices for six years. “In 2011 we saw the pattern that energy prices shot up in winter and fell slowly in summer, bearing little relation to wholesale energy market prices.

“Since 2011 the majority of customers on standard variable tariffs had been consistently overcharged by the big six. The amount overcharged has now topped £8bn. Ofgem has stepped in to protect pre-payment meter customers, but this market is failing every customer.”

Penrose is similarly emphatic. “Loyal customers are being systematically ripped off by big energy companies, and it’s just not fair,” he said. “Most industries don’t exploit their best customers like this, by quietly switching them on to expensive default tariffs when their existing deal comes to an end. Loyalty should be rewarded, not exploited.”

The MPs have the support of Citizens Advice. The consumer watchdog’s chief executive, Gillian Guy, said loyal customers were hit hardest by “the failures of the UK energy market”, with 2 million low-income families paying £141 extra every year.

“The government is right to say it will take action to fix markets that aren’t working for consumers. Extending the price cap on pre-payment meters to standard variable tariff customers who are eligible for the warm homes discount would be the first step to help some of those who can least afford rising bills.”

There are signs that the MPs’ campaign is gaining traction, with Penrose and Flint due to meet energy secretary Greg Clark on Monday. A spokesman for the Department for Business, Energy and Industrial Strategy said: “We expect energy companies to treat their customers fairly and continue to be concerned by recent price rises which will hit millions of people already paying more than they need to. Wherever markets are not working for consumers, this government is prepared to act.”

It wouldn’t be the first government that has intervened in the energy market, but few have had much success. Gas and electricity companies have been able to compete for customers since 2001, after the old regional electricity boards were transformed into the big six through a series of mergers.That led to the doorstep mis-selling scandals when customers were signed up to switch provider without their knowledge, ending in multimillion-pound fines for EDF, Npower, British Gas and SSE.

In 2008 price rises of 42% prompted Ofgem to hold an energy supply investigation, then in 2010 a retail market review.

Little had changed by the time David Cameron pledged in 2012 that energy companies would be forced to put customers on the lowest tariff, then tried to restrict suppliers to offering a maximum of four tariffs to simplify the market.

But government interventions may be part of the problem, according to Richard Neudegg, the head of regulation at uSwitch. “Tinkering with ideas like price caps as a magic bullet to bring down energy bills is a knee-jerk reaction that will leave consumers even more out of pocket in the long term,” he said. “Price caps may sound good on paper, but would remove the incentive for energy companies to drive down prices and fight to keep their customers. It would be a death knell for competition.”

The mere threat of government intervention was actually causing price rises for consumers, Neudegg said, because suppliers were withdrawing their best tariffs.

Then last year the Competition and Markets Authority announced a package of “remedies” to clean up the market and encourage the sticky 66% to exercise their consumer rights.

This included giving energy companies a database of about 10 million customers who had never switched, letting price comparison websites choose which deals they promote, and capping bills for pre-payment customers like Mckay who only have access to a fraction of the deals available on the open market. Neudegg said the CMA’s remedies “should be fully implemented and given time to succeed”.

Martin Lewis, the financial journalist who founded the Money Saving Expert website, said there was a fundamental problem with politicians trying to get the market to deliver solutions to social problems.

“It isn’t good enough to blame the energy companies for making money,” he said. “Their job is to make money for their shareholders. Politicians need to decide if they want to have a free market or if they want price controls. If we’re going to embrace competition, we need to accept that some people will pay more.”

Lewis also believes there is a growing problem with smaller suppliers who are being allowed into the marketplace without thorough checks on whether they are solvent.

Malinowski agrees, citing the failure of GB Energy, which went bust in November leaving 160,000 customers owed money for bills paid in advance. Ofgem gave their accounts to Co-operative Energy, but Malinowski believes there will be more collapses.

“It’s the volatility of the marketplace,” he said. “There are companies being founded with just £1 of capital. They get customers to pay upfront to give them capital, and they get free marketing from sites like ours to promote their product.” Ofgem has defended the entry of small companies into the market, as they can put pressure on the big six to reduce their prices.

The regulator hopes that smart meters will make the market more efficient, with more than 4 million installed so far. Estimated readings lead energy companies to create inaccurate bills, but with smart meters companies will be able to see exactly how much fuel is being used. Customers will also find it far easier to see how much electricity or gas they consume, and even which appliances use most energy.

An Ofgem spokesman said: “We want to see suppliers put under greater competitive pressure on pricing, especially on prices for customers on standard tariffs. We are concerned that the market is not as competitive as it should be, which is why we are bringing in reforms to help more customers get better deals.

“Suppliers need to justify to their customers why their prices are going up, or risk losing them as a result.”