A No 10 spokesman made clear that Mr Cameron was not seeking to tell people whether they should put on a jumper when temperatures drop.
But Mr Miliband said: "Their crime policy used to be 'hug a hoodie'. Now their energy policy appears to be 'wear a hoodie'."
Government advice to shop around for the best deal will not provide relief to consumers struggling with rising gas and electricity bills, said the Labour leader, who has promised to freeze energy prices for 20 months if he wins the general election in 2015.
Mr Cameron yesterday said that it was "disappointing" that British Gas had become the second of the "big six" energy companies to announce above-inflation price rises.
And he added: "There is something everyone can do, which is look to switch their electricity or gas bill from one supplier to another."
Energy Secretary Ed Davey last night added his voice to Government calls for consumers to switch providers and take energy-saving measures to reduce their bills.
And Mr Davey told BBC2's Newsnight: "I'm sure people do wear jumpers, I wear jumpers at home.
"We do need to help people with these bills, I'm extremely worried about them. We can use competition in the way we have but we can also make our homes warmer and we can use less electricity and gas by going energy-efficient, and that's what the Government is trying to do."
Asked at a daily Westminster press briefing today whether Mr Cameron agreed that people could reduce their fuel bill by wrapping up warm, the Downing Street spokesman said: "That's not a question that I have asked him. Clearly, he is not going to prescribe necessarily the actions individuals should take about that.
"But if people are giving that advice, that is something that people may wish to consider."
The spokesman added: "His advice to people is to shop around for fuel prices."
Writing on the Labour website, Mr Miliband said: "These responses to the energy price rises show how little Mr Cameron and his Government stand up for the interests of hard-working people.
"He has no grip on the cost of living crisis and he seems to think the solution to this crisis is nothing to do with him.
"Energy bills are already up by an average £300 since he took office. The price hikes we are seeing point to a market that isn't working for consumers. Yet his solution to this market failure was to tell people to shop around and dress warmly .
"Of course people will rightly seek the best deal they can find but that will not fix a broken market, and will not bring the kind of relief that consumers and businesses need."
Mr Miliband added: " Never let the Government tell you that there's nothing they can do, or that it's your responsibility to sort out the problems in our energy market.
"They could act - they just choose not to."
British Gas announced yesterday that it will hike electricity bills by 10.4% and gas tariffs by 8.4% for around 7.8 million families this winter.
The group is the second of the "big six" providers to announce price increases this month after SSE recently said more than seven million customers will be hit with an 8.2% rise from November 15.
A Downing Street spokesman later said: " To be clear, it is entirely false to suggest the Prime Minister would advise people they should wear jumpers to stay warm.
"Any suggestion to the contrary is mischief-making. The Prime Minister would point people to a range of things being done to help people with their fuel bills, such as legislating to put everyone on the best tariff for them. He believes Labour's "price freeze" policy is a con - and certainly would not advise people on what they should wear."