Mr Cameron added: "But there's something everyone can do which is to look to switch their electricity or gas bill from one supplier to another and on average this can help people save sometimes as much as £200 on their bills.
"So I'd encourage customers who are not happy with the service they're getting and not happy with the prices to go to the switching sites online and see whether they can get a better deal."
Meanwhile Ed Davey, the Energy Secretary, said that several energy suppliers are offering households a better deal than British Gas.
"I have said to British Gas customers that if they are worried about this they should change," Mr Davey told the Commons. "There are a range of competitors and alternative suppliers that are offering a much better deal. And by the way, those suppliers are there because of the actions of this Government."
British Gas' price hike comes just days after rival Scottish & Southern Energy announced an 8.2 per cent price rise. British Gas' gas rates will rise by 8.4 per cent, with electricity going up by 10.4 per cent, from November 23.
Mr Davey said the company would need to justify its decision to consumers.
"British Gas will need to justify their decision openly and transparently to bill payers," he added.
Caroline Flint, the shadow energy and climate change secretary, accused the Coalition of siding with the "big six" energy firms over increases to energy bills.
"This government can do something now," she said. "They were asked an hour ago in the House of Commons if we saw unreasonable price hikes would they tackle this and freeze the bill, and the answer was 'no'. Well, Labour is going to stand up for the public on this one we will challenge the energy companies, and we will change the market. This government, this prime minister, David Cameron, is only speaking for the energy companies."
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