Seven out of 10 families who receive supplies from food banks run by the Trussell Trust, a Christian charity, have dependent children, research by Sheffield University's political economy research institute found.
Almost 600 households with children under the age of 16 were surveyed, with four out of five classed as "severely food insecure", meaning they had skipped meals and gone without eating, sometimes for days, said the report.
Single parents using food banks were most likely to report rising food and housing costs.
Dr Rachel Loopstra, the report's lead author, said: "Our findings draw urgent attention to the severe food insecurity and poverty experienced by families with children who are receiving help from food banks.
"Low-income families with children have experienced significant reductions in welfare entitlements in recent years, and entitlements will be reduced further for low-income families given changes to child tax credits and the ongoing benefit freeze in the context of rising living costs.
"If financial support is not increased for low-income families with children, it is likely more children and their parents will need to use food banks in the years to come.
"Annual measurement of food insecurity in a national survey is needed to monitor vulnerability to this serious problem among households with children."
Trussell Trust chief executive Emma Revie said: "As a nation, we value justice and compassion, particularly for our children, but this research shows families across Britain are locked in poverty, with income so low they are unable even to afford to put food on their children's plates.
"These findings are particularly concerning when we are braced for further real-terms reductions in the very working-age benefits that should be protecting these families and children from poverty and hunger in the first place.
"Our network of food banks will continue to ensure food and support is given to families facing hunger right now, but we are also calling on Government to unfreeze working-age benefits.
"There should be no higher priority than ensuring all UK families can afford to put food on the table when their children are hungry."
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