Energy bills could rise by more than 60% within the next few years, said a report for the UK's biggest domestic energy supplier Centrica.
It says annual average gas bills could rise from Ј600 to more than Ј1,000 early in the next decade.
It says continuing high oil prices could lead to rises in the cost of both gas and electricity.
Centrica managing director Jake Ulrich warned that gas prices were likely to continue rising "for some time".
"I think it is going to hit people hard," he said.
"I do think we will see people change their behaviour, I think people will use less energy MPs set to question energy bosses ...
Energy bills could go up by 40% ... and I hate to go back to the Jimmy Carter days in the US but maybe it's two jumpers instead of one.
"I think people will change the temperature they keep the house, they'll be more cognisant of energy waste, they'll buy better appliances."
He added: "We're part of a world economy and I don't think we can rely on UK production or cheap gas, cheap energy of any sort any more.
"I think it's a reality not only in the UK but in Western Europe and North America. Energy is going to become relatively much more expensive in the future."
BBC News business reporter John Moylan says some people will wonder whether, by publishing the research, Centrica - which owns British Gas - is laying the groundwork for even steeper price rises in the years ahead.
The study - Under the Influence of Oil - was conducted for Centrica by Norwegian-based energy advisers Eclipse.
Eclipse managing partner John King said: "This report signals the significant change which the UK will go through over the next few years as the price of the UK gas market becomes influenced by factors across the globe."
Declining output
The report said that the link between crude oil prices and wholesale gas prices in the UK will get stronger over the next few years as dwindling output from North Sea makes the UK more dependent on imports.
The UK must now compete with European countries for gas transported by pipeline or bid for tanker loads of liquefied natural gas in international markets where prices are correlated with oil.
"As recently as 2004 we were entirely self sufficient but by 2010 half our gas will come from somewhere else," Niall Trimble, managing director of industry consultants The Energy Contract Company, told the BBC.
Oil prices, which hit a record above $147 a barrel earlier this month, have fallen sharply this week to about $133 a barrel but are still twice as high as a year ago.
"The gas spot market has risen very, very sharply in the past year and the spot market is driven by oil," Mr Trimble added.
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(BBC)
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