They likened the emergence of the new grouping to the ministry of John Wesley in the 18th Century which led to the creation of a separate Methodist Church.
Leaders of the so-called Gafcon [Global Anglican Future Conference] group of primates have been meeting in London for the last week to discuss plans for the future.
In a joint communique, the primates, who include the influential archbishops of Kenya and Nigeria, singled out concerns over the Church of England, including the recent Muslim prayer service in St John’s church in Waterloo as well as the case of a bishop facing an investigation over his role in setting up a new independent congregation.
Bishop John Ellison, a retired missionary, is under investigation in the Diocese of Salisbury after it emerged he is acting as an overseer for Christ Church, a new church in the city which describes itself as Anglican but operates outside the Church of England.
It is one of around a dozen new congregations affiliated to the Anglican Mission in England (AMIE), a traditionalist organisation widely seen as embryonic breakaway church in England.
“We continue to encourage and support the efforts of those working to restore the Church of England’s commitment to Biblical truth, “ the group said.
“Equally, we authenticate and support the work of those Anglicans who are boldly spreading the gospel of Jesus Christ and whose circumstances require operating outside the old, institutional structures.”
They added: “We are particularly concerned about the Church of England and the drift of many from the Biblical faith.
“We do not regard the recent use of a Church of England building for a Muslim service as a minor aberration.
"These actions betray the gospel and discourage Christians who live among Muslims, especially those experiencing persecution.”
Facing challenges: the Archbishop of Canterbury
Gafcon’s General Secretary, the Most Rev Peter Jensen, the former Archbishop of Sydney, said the new churches would help “renew” Anglicanism in England from outside the established church.
“I think we will have churches in place which will be regarded by most of the Anglican Communion as Anglican but not be Church of England Churches,” he explained.
“At the present moment we are looking at a handful, depending on how it goes – that might be it but who can tell?
“Things have happened in the last decade which have been truly astonishing, we are looking at a totally new age from the point of view of the cultural milieu around us.
“Christians are having to work things out which worked out for millennia.
"This might be the beginning of something as big as Wesley.”