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The energy regulator told the BBC that increasing prices, for gas in particular, "will feed into all customer energy bills in the UK".
It described the energy price cap as one of the "best tools" to ensure consumers pay a fair price.
But the price cap for default domestic energy deals has already been raised to cover rising wholesale costs.
The typical gas and electricity customer is likely to see their bill go up by £139 to £1,277 a year from October.
Prepayment customers, meanwhile, will see an increase of £153, from £1,156 to £1,309.
The price cap limits the price that companies can charge customers who have not recently changed their tariff or energy supplier and allows them only to charge legitimate costs.
"We have put tough rules in place to ensure suppliers treat customers who are struggling with bills fairly, and welcome their commitment to reach out to those who most need help," an Ofgem spokesperson said.
"Where help is not forthcoming, we will not hesitate to act," the watchdog added.
Lisa Barber, home products and services editor at Which?, warned that if the wholesale cost of energy continued to rise, those on variable tariffs might see their bills increase and the number of cheap tariffs on the market might shrink.
To keep costs down, Which? suggests:
- Switching energy providers regularly
- Signing up to a fixed tariff to keep bills stable
- Installing heating controls such as room thermostats and thermostatic radiator valves
- Using energy-efficient appliances
It comes after the UK had to fire up two old coal power plants to meet electricity needs earlier this week.
Warm, still, autumn weather has meant wind farms have not generated as much power as normal, while spiking prices have made it too costly to rely on gas.
On Tuesday, the use of coal returned to 2.2% of the UK's electricity generation.
Audrey Gallacher, Energy UK's deputy chief executive, said: "Due to the unprecedented price increases in natural gas, National Grid, the electricity system operator, has had to make some tough choices about where we get our power from in order to maintain security of supply.
She said the move highlighted the "need to continue the low carbon energy transition, and further reduce our dependency on fossil fuels for our heat and power".
"It will not only help us meet climate change targets but remove the risk of being exposed to volatile international wholesale prices."
Energy UK added that it "recognises" the impact increased energy prices would have on customers and that anyone worried about their bills should talk to their supplier.
Some suppliers have said that profits have been hit by financial assistance offered to customers struggling to afford the higher prices.
Robert Buckley, and energy analyst at Cornwall Insights, said prices for power which is needed immediately are at all-time highs - 10 times the prices of last summer.
"There's very high international commodity prices for gas and for carbon as economies recover from Covid, and the EU has tightened up its carbon market rules," he said. "Very high coal prices as well."
"In the UK we've a combination of low wind, we've had outages at some of the nuclear stations, some of the gas stations have been offline, and we've had lower flows into the country of gas from Norway," he said.
Consumers will see these rises push their bills up this winter as the price cap goes up, but if wholesale energy prices continue at these highs the cap "will go up a lot more".
However, in the meantime the high prices are "also very bad for suppliers because the cap limits what they can charge their consumers, and the market is way above that now", Mr Buckley added, saying it was "very sad" that some small suppliers had already gone out of business.
Source: BBC News