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The Fathers4Justice campaign group has listed this week’s Lambeth Conference as a possible target for protest.
More than 600 archbishops and bishops from all over the world will converging on Canterbury from Wednesday for the 20-day conference.
Darren Ash, Fathers4Justice Kent organiser, from Herne Bay, said the meeting was in his group’s “pipeline.”
He would not be drawn on any plans but said: “It’s on the list but I cannot say whether anything will happen.
“The decision is made by head office, who know things they want to target.”
The group campaigns for a child’s right to see both parents and grandparents when a relationship breaks done.
Mr Ash says he has not seen his daughter for more than two years.
The Lambeth Conference is itself shrouded in controvery following the Church Synod vote on the ordination of women bishops which led to the Bishop of Dover breaking down in tears.
Bishop in tears after Synod vote>>>
Around 150 bishops are also boycotting the conference over the issue of homosexual clergy.
Delegates are staying at Kent University, where many of the meetings will be held.
There will be a service at Canterbury Cathedral on Sunday, July 20, led by the Archbishop, Dr Rowan Williams.
Conference delegates will also attend services at 65 parish churches in the Canterbury Diocese on Sunday, July 27.