The clerics, along with members of different faith groups are concerned it will hit low earners the hardest and could even lead to more abortions.
Under the policy parents can no longer claim tax credits from the state after their first two children.
The Bishops suggest by 2021, 640,000 families will have been affected.
Writing in the Times about the policy, the leaders which include new Bishop of London Rt Rev Sarah Mullally say: "It conveys the message the regrettable message that some children matter less than others, depending on their place in the sibling birth order.
"It is a grave concern that there are likely to be mothers who face an invidious choice between poverty and terminating an unplanned pregnancy."
In response, the Department for Work and Pensions said: "[The policy] will be delivered in the most effective, compassionate way, with the right exceptions and safeguards.
"But it's right that people on benefits have to make the same financial choices as those supporting themselves solely through work."
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