Millions of people are over-paying for gas and electricity because of excessive price rises by the big six energy companies, the government has admitted, as MPs of all parties demand action to stop them “ripping off” customers.

Ahead of a key debate in parliament on Thursday, in which a cross-party group of MPs will call for drastic measures to control the market and protect consumers, the Department for Business, Energy and Industrial Strategy said ministers were ready to act where the market was failing.

In a statement to the Observer, the department said it was vital consumers were treated fairly. It said ministers were “concerned by recent price rises, which will hit millions of people [who are] already paying more than they need to. Wherever markets are not working for consumers, this government is prepared to act.” So far this year three large companies have announced price increases of just under 10% on dual-fuel standard variable tariffs, adding about £100 a year to customers’ bills. Last month Npower announced an increase of 9.8% and last week E.ON said it was raising charges by 8.8% from April.

EDF raised electricity prices in December but cut gas prices, amounting to a 1.2% increase. SSE will announce its plans at the end of this month, while British Gas has said it will freeze prices until August. Several medium-sized suppliers have also raised prices: Good Energy, up 11%, First Utility, up 9.7%, Utilita, up 2.9%, Co-operative energy, up 5%, and Ovo Energy up 1.5%. The latest increases come despite the energy regulator Ofgem recently saying it saw no reason for the big six to raise prices despite upward price pressures, because of the way they hedge when buying power.

Pressure on the government to step in is mounting from MPs, who say Theresa May can go a long way to honour her commitment to help the less well-off by addressing the issue of energy bills, which Ofgem says now account for 10% of spending in the poorest households, compared with just 5.5% in 2004.

The three MPs who have secured the debate on Thursday – former Tory minister John Penrose, Labour’s Caroline Flint and the SNP’s Patricia Gibson – are being backed by at least 50 colleagues across all parties. Penrose said customers were often being switched on to expensive standard variable deals without their knowledge, once their lower tariff periods expired. “Loyal customers are being systematically ripped off by big energy firms, and it’s just not fair. 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.” Penrose will propose a new “relative price cap”, under which customers cannot be transferred to a new deal more than 6% more expensive than their expired one.

A recent report into the energy market by the Competition and Markets Authority, commissioned by David Cameron before the 2015 general election, found customers had paid £1.4bn a year in “excessive prices” between 2012 and 2015, with those on standard variable tariffs (70% of the total) paying 11% more for their electricity and 15% more for their gas than customers on other tariffs.

Flint, a former shadow energy secretary, said action was needed to ensure all customers were given the same protection as those on pre-payment meters, who were protected by caps. “This has been a six-year campaign for fair energy prices. 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 had now topped £8bn. “Ofgem has stepped in to protect pre-payment meter customers, but this market is failing every customer. 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. This cannot go on.”

Most of the firms cite rising wholesale prices for the increases, while E.ON said it has seen a drop in wholesale costs and instead attributes the increase to government schemes such as renewable energy subsidies, levied on household energy bills.

The motion to be debated on Thursday states that the House “deplores the big six energy firms’ treatment of out-of-contract energy customers on default tariffs; believes immediate action is needed to protect these consumers, and that pushing customers to start switching will not fix the problem sufficiently quickly or completely on its own; and calls on the industry, regulators and the Government to consider solutions which recognise that many people lead busy lives where switching their energy supplier may not always be a high priority.” MPs can push the issue to a vote if they conclude that the response from government has been unsatisfactory.