Other energy suppliers must follow and improve upon E.ON's "long overdue" move to cut its standard gas price to reflect falling wholesale prices, consumer groups have said.
E.ON is to cut its standard gas price by an average of 5.1% from February 1, which it says is the equivalent of £32 off an average annual gas bill.
The announcement comes as wholesale prices for gas and electricity fell to their lowest level for five years and follows mounting criticism that companies are failing to pass the drop on to customers.
Citizens Advice chief executive Gillian Guy said that while E.ON's cut was encouraging, the savings for customers would be "modest" and the energy giant also needed to lower electricity bills.
She said: "The industry as a whole urgently needs to step up to the plate - suppliers need to play fair with customers and start passing on the major savings they have been making from cheap wholesale costs."
Which? executive director Richard Lloyd said E.ON had taken the first step by cutting its prices for gas deals "but given plummeting wholesale costs, consumers are bound to question if it's enough".
Price comparison website USwitch also said E.ON's customers may feel "underwhelmed" by the size of the cut.
Ann Robinson, USwitch's director of consumer policy, said E.ON's move was "long overdue" and added that bill reductions of at least 10%, or around £120 a year, on gas and electricity would more accurately reflect the fact that wholesale prices were at a five-year low.
The mild winter and lower commodity prices have led to further drops in wholesale gas and electricity costs, according to the ICIS Power Index, which analyses energy markets.
The report, released last week, said UK power prices finished the year at five-year lows, and were down 23% over the year.
Energy and Climate Change Secretary Amber Rudd wrote to energy firms in the middle of last year asking them to pass on a fall in wholesale costs to consumers.
Ofgem chief executive Dermot Nolan said: "This is a step in the right direction and it is good to see some movement in energy prices for consumers.
"We have consistently called on suppliers to explain why retail prices are not falling and this price cut goes some way towards addressing that challenge."
E.ON said the new tariff - a one-year fixed dual fuel deal with an average annual price of £783 - would be "Britain's cheapest energy tariff available today".
E.ON chief executive Tony Cocker said: "The underlying position is that, whilst the price we pay for our customers' energy has fallen, we also have to take account of managing the various other risks in the market which can change, and the fact that many of the other costs that we don't control but do have to bear have increased or may increase.
"Once you've built in various uncertainties and other factors, whilst the wholesale market movements may translate across to a dual fuel domestic bill for a drop in prices of under 10%, the inclusion of those other factors translates the percentage to the standard gas cut announced today. We will continue to keep all these factors under review."