The big six energy firms have been exposed to further accusations of profiteering after the industry regulator revealed that profits per customer last year rose by 77%.

On the eve of a protest by anti-poverty campaigners against power suppliers, Ofgem said the profit per household had risen from £30 in 2011 to £53, driven by higher prices and increased demand for heating during last year's winter snap.

The average profit margin for supplying energy to households in 2012 was 4.3%, up from 2.8% in 2011, with total profits from supplying energy to households and businesses rising from £1.25bn to £1.6bn last year.

"Any profit margin at a time when people are dying because they cannot afford to turn their heating on is unacceptable," said Clare Welton at the Fuel Poverty Action group, which will mark the publication of the latest winter mortality figures on Tuesday with a protest at RWE npower's headquarters in central London. Protests will also be held at the new British Gas headquarters in Oxford. Alex Smith, a spokesperson for UK Uncut, a co-organiser of the protests, described the latest data as unsurprising. "We have seen nothing but profiteering from the big six," he said.

The big six – British Gas, npower, SSE, Scottish Power, E.ON and EDF – argue that their industry is misunderstood and higher bills are the inevitable consequence of external factors such as green levies passed on by the government, higher wholesale prices and increased power transmission costs. However, the industry's trade body admitted this month that the big six had become a "lightning conductor for the general concern about the cost of living."

As a result, the companies have faced cross-party condemnation for average increases to consumer bills well above inflation. Labour leader Ed Miliband has pledged a price freeze, while former prime minister Sir John Major has called for a windfall tax on profits. The Ofgem data does not cover profits related to the latest series of price rises, which has reignited the debate about whether the big six make "fair" profits.

Ofgem said rising prices, rather than lower costs, were a factor in the profit increase. "There is some evidence of rising profit margins. This rise has been due to a combination of higher prices and volumes rather than lower costs," said the regulator.

But Richard Hall, director of infrastructure at Consumer Futures, a consumer watchdog, said Ofgem had "produced a lot of evidence that would persuade a third party that there is a trend [of rising prices]".

He pointed out that other Ofgem data showed "a steady escalation in profit". The regulator's own forecast data shows an average profit per customer of £105 in November 2013.

Caroline Flint, Labour's spokesperson for energy and climate change, said the Ofgem report showed why a price freeze is needed: "Labour's price freeze will save money for 27 million households and 2.4 million businesses and our plans to reset the market will deliver fairer prices in the future. People are sick and tired of paying over the odds because David Cameron is too weak to stand up to the energy companies and just stands up for a privileged few."

A spokesperson at the Department for Energy and Climate Change said: "Profits are a matter for energy companies to justify to their customers and shareholders, but profits are needed if they are to continue to invest in Britain's energy security and infrastructure."

Although energy companies have been making more money from supplying households, overall profits were down 3.4% in 2012 on the previous year, from £3.7bn to £3.9bn, as firms were hit by depreciation costs and declining profitability from their gas-fired power stations.

Consumer groups are calling on Ofgem to compel energy companies to publish financial information closer to real time. The regulator has been criticised by MPs for dismissing recommendations from its own consultants to make the energy market work more transparently. Ofgem had "room for significant improvement" said Hall. "It feels as though we are only now starting to see the implementation or possible implementation of changes that we could have been done a couple of years ago."