Younger consumers aged between 16 and 34 are the most concerned, at 53%, together with women, at 52%, according to research by analysts Mintel.
Concern peaks in the colder regions of the North West (51%) and the North and Scotland (49%) compared to 43% in the South East and East Anglia.
And the poll suggests that it is not just an issue for the worst-off households. While concern is highest among those on lower incomes, at 60%, payment is also an issue for more than a third (35%) of better off consumers.
Almost six in ten Britons (58%) agree that it is important to regularly check that they are on the best tariff, while 44% worry they are not on the best tariff.
Overall, more than half (56%) admit that they find their energy bills confusing.
Mintel senior retail analyst Jane Westgarth said: "Escalating domestic energy bills can take a large chunk of the household budget, particularly for low earners, so making it easier for people to manage their usage and spending will help to reduce the anxiety surrounding paying the bills.
"People find the appeal of fixing prices very compelling as it takes away some of the uncertainties about how their bills will change and reduces the concern that the direct debits might escalate or that bills will become unaffordable. So marketing that builds reassurance about being able to plan ahead and avoid unexpected bills will chime with people."
Some 73% of Britons agree they should make their home as energy efficient as possible, but 48% say they worry that it will cost too much money.
Almost two thirds (65%) of Brits say that wasting energy in the home is a big concern for them.
And it found that 43% of consumers worry that using too much energy is bad for the environment, however just under a quarter (24%) agree that it is worth paying more for greener energy.
Ms Westgarth said: "For the majority of consumers, acting to get greener energy is secondary to finding the best deal on price. While consumers are aware of environmental issues, this may not affect the way that they act or choose which power to buy.
"When it comes to the environment, many would prefer the state to make the big changes but do not necessarily think it is something they can influence themselves."
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