British Gas has the largest share of the country's gas domestic supply market and, according to Davey, has charged households among the highest prices over the past three years – while being on average the most profitable energy provider.
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Davey called on Ofgem to consider whether this merited a market investigation – and named one of the potential solutions being a "break-up of any companies found to have monopoly power to the detriment of the consumer."
British Gas came under fire in October last year when it announced plans to raise household energy prices by an average of 9.2 percent - 8.4 percent on gas and 10.4 percent on electricity.
Centrica subsequently cut its earnings forecast for 2013, warning that growth in adjusted earnings per share would be flat – down from growth forecasts of 3-4 percent.
The company's shares were around 3 lower in mid-morning trading on Monday. Over the past six months, Centrica stock has lost around 20 percent of its value amid ongoing controversy about rising energy bills.
Meanwhile, shares in U.K. energy company SSE – another of the "big six" utilities which dominate the British market – were down over 1 percent on Monday.
The letter comes amid an annual assessment of the energy market by the Office of Fair Trading (OFT), Ofgem and the Competition & Markets Authority.
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In a statement, British Gas said: "We welcome this (assessment) and have complied with all the requests for data which we have received.
"Further discussions have been arranged over the coming weeks in which we will fully participate. The data referred to in the Secretary of State's letter has already been fully disclosed and in the public domain for a number of months."
In his letter to Ofgem chief executive Andrew Wright, Davey stressed that there should be a shift in focus from electricity prices to gas prices, which make up two-thirds of the energy bills in 85 percent of households.
"The gas market has little vertical integration and analysis of the profit margins of the energy companies shows that the average profit margin for gas is around three times that of electricity," he wrote.
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"For some companies the profit margin is actually more than five times the average profit being made on supplying household electricity."
He added that if the profit margin in the domestic gas supply market was similar to that in the electricity market, an average household would save up to £40 ($66) a year.
Consumer organization Which? described Davey's letter as a "hugely significant intervention" and added that the structure of the biggest energy companies was partly to blame for the energy price hikes.
"The pressure is now on the regulators to announce next month that they are taking the first steps towards a more radical reform of the energy market, and to give consumers confidence that they are paying a fair price," Which? executive director Richard Lloyd said in a statement.
Britain's opposition Labour Party responded to the letter by repeating its calls for a price freeze "to stop these firms from overcharging in the future." Labour has previously pledged to freeze prices for 20 months if it won the 2015 general election.