In a statement, they said that while they've chosen not to make political statements around Brexit the risk to the poorest families across the UK compels them to speak up.
In a strong worded statement, they said: "As Christians we are called to demand justice for the millions locked in poverty. A No Deal Brexit risks tightening poverty's grip on families up and down the country.
"Over the past decade, our churches have witnessed and responded to the slowly rising tide of hunger in the UK. A no-deal Brexit risks restricting the nation's supply of food and increasing prices. This, alongside further cuts to benefits on Monday 8th April, could have grave consequences for many in our communities.
"Many charities are warning us that food supplies to the most vulnerable are most at risk - hospitals, prisons and those reliant on surplus or donated food. Supplies of essential medicines are likely to be disrupted. Again, the most vulnerable will be the least able to cope with this."
The three church groups represent a combined membership of 350,000.
Explaining the reasons behind the statement on Premier's News Hour on Friday, Paul Morrison from the Joint Public Issues Team (which represents the three churches) said: "We already see people coming into our churches who are hungry and who need the help of food banks.
"The last thing we want to see is more people in that position needing that sort of help. So we are speaking out now because we really have no choice."
The intervention comes as Theresa May formally requests to delay Brexit until the end of June.
Her plea will be considered at an emergency European Union summit next week.
The prime minister also wants an option to leave sooner if MPs back her withdrawal deal.
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