Around two out of five families would fall into debt if the cost of their energy increased, according to a household financial confidence survey.
If energy bills increased, 44% of families with children at home believe that it would push them into debt with their energy provider.
This is double the proportion of families without children in the house, at 22%, comparethemarket.com found.
The research found that annual energy costs would only have to increase by an average of £85 to tip households with children at home into financial difficulty.
One in six (17%) families with children at home are in arrears to their energy provider, or have been, in the last 12 months and nearly one in 10 (9%) are still in the red, the research found.
Nearly three in 10 (29%) are not currently in debt but are worried they could soon fall into arrears. By contrast, only 8% of families without children at home are concerned about energy debt.
Over a quarter (26%) of families with children at home said they had struggled to pay their bills over the previous week and 23% said they were worried about their ability to meet their financial obligations over the coming weeks.
This compared with 13% of families without children in the house who said they were worried.
Peter Earl, head of energy at comparethemarket.com, said: “Families have faced significant financial challenges throughout the pandemic, but this winter has hit budgets especially hard when it comes to energy bills. The added costs of more people in the house, both for work and schooling, means households with kids could be facing one of the most expensive quarters on record for energy.
“The focus must not just be on rebuilding businesses and the wider economy but must also pay attention to how people can rebuild their finances after such a difficult year.
“There are simple ways households can save money on their energy bill, including shopping around for a new deal. Households who are in debt and struggling to pay their energy bills should speak to their energy supplier to see if there is a cheaper tariff they can move to, or any help available to them such as the Government’s cold weather payments.”
More than 2,000 people were surveyed across the UK between February 19 to 21.