Three in five people (58%) are worried about the effect that higher bills will have on their finances and 53% - or 27 million - will have to cut spending to cope, according to a study by the consumer body.
The survey found that of those who plan on cutting their spending, 59% say they will have to reduce the amount they spend on food, 37% will look for ways to reduce their energy bills, 8% will consider moving to a cheaper home.
A further 66% say they will have less to spend on time out.
It found 20% of British households are struggling or falling behind with their bills while a further 32% said they are keeping up with costs, but it is a struggle.
Of those concerned about paying their fuel bill, 55% have cut down the amount of energy they use, 36% have spent less on food, 34% have sacrificed leisure activities or spending time with family and friends, 15% have gone into their overdraft to pay their energy bills and 11% have borrowed money from family and friends.
The poll also found that less than one-third of people (28%) have spoken to their energy supplier to check that they are on the best tariff.
Citizens Advice chief executive Gillian Guy said: "We're keen to make sure people are not taking drastic action or paying a penny more than they have to for a warm home or to keep the lights on."
"Through Big Energy Saving Week, Citizens Advice is helping consumers to check, switch and insulate."