The survey of 4,000 adults also found that more than one in four families (27%) cut back on gas and electricity bills to help meet their rent or mortgage costs.
Across the population as a whole a third of people (31%) had cut back on food and one in five (20%) had reduced their household fuel spend.
The research also found that 64% of families with children struggled to pay for their rent or mortgage last year, compared to 57% of people across the board.
Campbell Robb, chief executive Shelter, said: "These startling figures show the daily heartache millions of parents are going through as they face the choice between putting food on the table and paying for the roof over their head.
"The effects of the recession, the rising cost of housing and cuts to the housing safety net have left many families in a very vulnerable position. Every fifteen minutes a family in England finds themselves homeless.
"We've seen more and more people coming to us for help in the last six months. For thousands of people already desperately battling to keep their home and further benefit changes next month could be the final blow.
“Anyone whose home could be at risk needs to get advice as soon as possible. Shelter can help prevent more families going through the devastation of losing their home."
