The Church of England and Child Poverty Action Group's new study has also found parents are being forced to drop children's activities like swimming lessons.
Tom Sefton, co-author of the report and social policy advisor for the Church of England told Premier many parents are not aware of the rule.
"The majority of the people that we spoke to - and I suspect this is true of many of your listeners - were not even aware of the two-child limit policy until it hit them and their family.
"So every day 200 more families are being affected by this policy and most of these are low income working families who rely on tax credits and Universal Credit to top up their earnings at a time in their lives when they've got very young children and they need that support."
The report includes a projection that one million children who already live in poverty will be pushed further below the poverty line by the time Universal Credit is fully rolled out in 2023/24, as a result of the two-child policy.
A survey of more than 430 families affected by the policy found that some parents felt "shame" at not being able to provide for their children's needs.
Sefton said they heard from "mothers who are having to borrow to pay for nappies and milk for their children, parents who are going hungry to make sure they can feed their children and families who are getting into rent arrears and at real risk of losing their home as a result of this policy".
The Rt Rev Paul Butler, Bishop of Durham, said the two-child benefit policy must be removed to "reverse the rise in child poverty".
"We believe that children are a blessing, not a burden, and that a third or fourth child is no less precious than the first or second," he explained.
"The Government's two-child limit goes against this fundamental principle and is pushing many families and children into poverty.
"It is simply not right that some children get support and others don't.
"The two-child limit must be lifted as part of a concerted effort to reverse the rise in child poverty."
Listen to Premier's Ruth Sax speaking to Tom Sefton:
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