But the Prime Minister insisted the Government was already doing what it could to try to keep costs down.
The comments came in a round of local radio interviews after British Gas announced that 7.8 million households face a 10.4% rise in electricity prices and 8.4% for gas tariffs from next month.
The Centrica-owned energy giant said average customer dual-fuel bills will rise by £123 to £1,444 a year according to Ofgem usage figures after the price increases, which take effect on November 23.
The group is the second of the "big six" providers to increase tariffs after SSE recently announced an 8.2% rise from November 15.
Mr Cameron told BBC Sussex radio: "I think it is a very disappointing announcement by British Gas.
"I think there are things we can do. We are intervening because we are legislating to say these companies have to put their customers on to the lowest tariff.
"I think a lot of customers find it utterly baffling how many tariffs they have.
"But there is something everyone can do, which is look to switch their electricity or gas bill from one supplier to another.
"On average, this can help people save sometimes as much as £200 on their bill.
"So I would encourage customers who are not happy with the service they're getting, are not happy with the prices, to go to the switching sites online and see whether they can get a better deal."
Pressed on whether the Government could do more to tackle the underlying issues, Mr Cameron said: "What we can do, which is what we are doing, is to try to get new suppliers into the market."
Regional variations mean some Scottish customers will see prices rise on average by as much as 11.2%, while those in London will suffer a 10.6% increase and households in Yorkshire will have a 10.5% lift.
The move comes despite a pledge by British Gas earlier this year to use an annual earnings windfall from the cold weather to keep a lid on tariffs.
British Gas hiked tariffs by 6% last November ahead of a bitterly cold period when gas consumption rose 18% in the first four months of this year compared to 2012 - helping earnings at its residential arm to rise 3.2% to £356 million for the first half of the year.
The company said in May that because of the economic pressures facing many customers, the board had decided that any benefit from the exceptionally cold weather would be used to maintain ''price competitiveness''.
Today it blamed the hike on the increasing cost of wholesale energy prices, Government energy initiatives and higher network charges for delivering power to customers' homes.
Ian Peters, managing director of British Gas Residential Energy, said: "We haven't taken this decision lightly, but what's pushing up energy prices at the moment are costs that are not all directly under our control, such as the global price of energy, charges that we have to pay for using the national grid that delivers energy to the home, and the cost of the Government's social and environmental programmes."
The group is also introducing a new fixed standard charge of 26p a day for all customers - which will impact another 6.1 million - and a single variable unit rate, depending on usage and tariff.
Consumer groups warned other providers are set to follow suit with price rises, leaving some households to choose between "heating and eating".
Martin Lewis of MoneySavingExpert.com said: "This price hike round is big, and is nasty.
"It also means that two of the big six sheep have bleated, the rest are likely to follow within the next six weeks, leaving millions more homes already under the cosh having to choose between heating and eating."
Energy Secretary Ed Davey said unhappy British Gas customers should quit the firm and buy their gas and electricity elsewhere.
He added: "This is extremely disappointing news for British Gas's customers and the company will need to justify this decision openly and transparently."
Minutes after British Gas confirmed the rises, shadow energy secretary Caroline Flint demanded to know what the Government would do about it.
Mr Davey said: "British Gas was the only company not to meet its targets under the previous obligation to make its customers' homes more energy efficient. That left more homes cold and their customers paying over the odds.
"British Gas has form in failing to meet its targets, the last ones set by Labour. I hope you can join with me in making sure British Gas is more transparent about its costs.
"We are pushing competition and I would urge customers of British Gas who are unhappy to change their supplier."
Ms Flint had used the announcement to renew her challenge to the Government on energy prices.
Speaking during the regular Commons questions to the Department for Energy and Climate Change, she said: "During the course of these questions, British Gas have announced that from November 23, they will increase their gas prices by 8.4% and their electricity prices by 10.4%.
"This is the company that, with Centrica, has passed on the highest share of its profits to its shareholders while at the same time making the least amount of investments into what we need to ensure our energy security in the future.
"Two years ago the accountancy firm BDO warned the big six energy companies could be under reporting their profits and they recommended tighter rules. But the Government and Ofgem failed to act.
"We back the new rules and so did a recent select committee report but, in their response, all the Government could say was 'Government is not in a position to comment'.
"Why won't you stand up for consumers, support Labour's price freeze and make the energy companies tell us exactly how much money they are earning?"
Labour MP Gregg McClymont (Cumbernauld, Kilsyth and Kirkintilloch East) asked: "Your response regarding the announcement of British Gas's rise in energy prices... can you explain how British Gas increases its operating profit by nearly £1.6 billion, announced in June 2013, and yet we now find (people) around the country will see their prices rises by between 8% and 10%?
"How can that be fair to the consumers of this country and when is the Government going to get a grip on this and finally do something about it?"
Mr Davey replied: "We are doing things about it - not only promoting competition and urging people unhappy with their suppliers like British Gas to change and choose because there are plenty out there, thanks to this Government, not thanks to your government.
"But we are also making sure the energy companies are more transparent and I would urge British Gas to publish and be more transparent about the increased policy costs it is blaming for these bill rises.
"We have looked at their initial figures and we really question whether their policy costs, which they claim are putting up the bill, are the root cause."