Scottish and Southern Energy (SSE) is putting up its domestic gas tariffs by 9.4% at the start of December.
The company, one of the UK's biggest energy suppliers, said the rise would affect 3.6 million customers.
The company blamed the increasing wholesale cost of buying gas which it said had gone up by 25% since March this year.
The company said it was sorry that the higher bills would come in during this winter.
"The last few months have been marked by rising wholesale gas prices and, having absorbed losses in our gas supply business for some time, we can not delay an increase in retail prices any longer," said Alistair Phillips-Davies, of SSE.
"I am sorry it will take effect during the winter period."
Those affected include 380,000 customers in Scotland and 440,000 customers in Wales.
The company said that people were being more careful with their energy consumption, so it calculated the price rise would be £4.64 a month for the typical customer, or £56 a year.
However, taking regulator Ofgem's standard consumption measure, the effect would be a £5.60 a month rise, or £67 a year.
This is the first time for two years that standard prices among the "big six" energy suppliers have risen, and follows some price falls during last year.
After 1 December, SSE customers with a dual-fuel tariff would still be paying bills that were £33 cheaper than when prices were at their peak in January 2009, said Ann Robinson, of Uswitch, but she said the timing was a concern for customers.
"With winter about to kick in, this is a body blow for consumers. What nobody wants to see is a repeat of 2008, when suppliers last put prices up and bills rocketed by £381 or 42% as a result," she said.
There could be more bills rises to come.
Earlier this month, Ofgem said that gas and electricity bills would both have to rise by £3 a year, as £32bn was needed to improve the UK's distribution infrastructure.
Ofgem said energy firms needed to spend that sum over the next 10 years to "keep the lights on" and meet the government's green energy targets.
Customers of the other major energy providers will have to wait to see if the rest of the industry also puts up prices.
"While we hope that other companies do not follow suit, history has shown us they adopt a pack mentality on pricing," said Audrey Gallacher, of watchdog Consumer Focus.
The watchdog has argued that companies should have reduced prices when wholesale costs were lower.
It claimed that SSE's gas prices had fallen by 2% since wholesale costs peaked in 2008, while the wholesale gas price had declined by more than 40%.
A spokesman for the Department of Energy and Climate Change said: "While, on behalf of consumers, we are disappointed in the decision taken by SSE to increase their gas prices, this is a decision for the company which must compete for customers in the marketplace.
"Consumers should therefore continue to assess regularly whether they are getting the best energy deal for them and to take steps to switch supplier and tariff if not."