Backed by the Archbishops of Canterbury and York, the plan is for people to: "get together and chat over a cup of tea and pray for our country and our future'.
Churches will be given packs with Bible-passages and questions to prompt discussion, such as: 'What effect has Brexit had in your family relationships, friendships etc and if you disagreed, has it been possible to disagree well?' and 'What are the three main things we have in common that we can build on for a better future as a community and as a nation?'
Bishop of Chelsmford, Rt Rev Stephen Cottrell, told Premier: "This process that we're embroiled in, which appears to be unravelling right now and will probably change again tomorrow - there will come a point where it comes to an end, when we wake up on that day we're still neighbours to one another and the thing that distresses me is that we're defining ourselves so much now by 'are you leave?', 'are you remain?', we've got to put an end to that and say whichever way you voted...we're still sisters and brothers to one another!"
He added that the cafe will be focussing on how to move on with a healthy attitude towards people with different opinions: "The conversation is not about Brexit but about how we can love one another, how can we be good neighbours to one another?
"Brexit has created a situation in this country which I don't think we've seen for years where we are divided and that's not a healthy thing.
"Come along to your local church and you'll get a warm welcome".
Those taking part will be encouraged to have respect for the integrity of differently held positions and, for communities which feel the same about Brexit, to use their imagination to consider the viewpoints of those who feel differently.
The Archbishop of Canterbury, Justin Welby, said: "A century from now the Church will be remembered for how it responded at this crucial moment in the life of our nation and country. Will we be those who worked to defuse tension and hostility? Will we be those who called for civility and respect in how we speak about, and treat, each other? Will we be those who never stopped praying with urgency and hope for our country, our communities and our political leaders - and for a way forward that allows every person, family and community to flourish?
"This is an opportunity for the Church of England to join together in prayer for God's kingdom to come, and for the good of all in society. I hope that each of us will take hold of these resources to help us pray for our country at this critical time."
The Archbishop of York, Dr John Sentamu said: "St Paul advises and urges Timothy to 'offer petitions, prayers, intercessions, and thanksgivings for everyone, for sovereigns, and for all in high office so that we may lead a tranquil and quiet life, free to practice our religion with dignity. Such prayer is right, and approved by God our Saviour, whose will it is that all should find salvation and come to know the truth.'"
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