This has prompted fears that parents are not saving enough to pay for their children's education or for any unexpected costs. A total of 28 per cent of the 2,000 respondents said they had no money put aside at all.
Figures suggested that the average bill for a three bedroom semi-detached house is around £831 a year for electricity and £800 for gas.
Reza Attar-Zadeh, director of savings and investments at Abbey, said: "It's vital for everyone to have a rainy day fund, even more so for parents, who must juggle the need to build up a nest egg for their children's future with the need to provide for the here and now."
In the first two quarters of 2009 the Citizens Advice Bureau reported a 46 per cent rise in consumers with fuel debt. It recommends shopping around to find the best deal on gas and electricity.
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.