More than a quarter (27%) of 853 parents of under-18s said they had cut winter spending to meet housing costs. 10% told researchers they feared being unable to pay rents or mortgages in January.
A shortage of affordable homes has left families struggling with sky-high housing costs, says the charity, while last year more than 100,000 people phoned its helpline for housing debt advice.
"We cut back on everything to pay the rent, including food," said Michelle, a mother from Cambridge. Her husband Kevin, a builder, became self-employed last year and is now paid weekly. The change in circumstances means the family are already in arrears on their rent to a private landlord and council tax. They fear missing more payments could put them at risk of eviction.
Some 15% of the parents interviewed also said they had to economise on Christmas food and gifts.
"Even though my husband works as many hours as he can, it's constantly hand to mouth," said Michelle, a student midwife. "When the children are at school, the heating isn't on at all, and over Christmas we had to cut back on presents and clothing," she added.
A Department for Communities and Local Government spokesman said: "The reality is mortgage repossession claims continue to fall and are their lowest since 1987. This is thanks to our work to tackle the deficit and keep interest rates low, helping more families to stay in their hard-earned homes. We've introduced measures to ensure tenants get a fair deal and are aware of their rights. We've also doubled the housing budget to deliver over 400,000 affordable homes and the number of new homes is up 25% in the last year."
The survey of a representative and weighted sample of adults was carried out online by YouGov late last year.