It is the African way. Tribal leaders settle their differences by sitting around a campfire for hours, and sometimes days, in a ritual exchange of ideas, following a process handed down by their forefathers.

But will it work in Kent? Yesterday the Archbishop of Canterbury invited hundreds of feuding bishops to an Anglicised version of the indaba, to talk not about stolen cattle and territorial disputes but about sexuality.

The early signs were not good. “If indaba is such a great idea, why is Africa such a mess?” one bishop is supposed to have said, although he denied it yesterday.

Dr Rowan Williams invited 650 bishops attending the ten-yearly Lambeth Conference at Canterbury to choose from one of several indaba groups, a key part of the next fortnight’s agenda. These meetings, named after a Zulu word meaning a gathering for purposeful discussion, had several themes: sexuality, heresy, Judaeo-Christian relations, ecumenicism, shared mission in Europe.

Times Archive, 1896: The last indaba with the Matoppo chiefs

Mr Rhodes said: "You are all so jealous of one another that I cannot appoint one induna to take the place of Lobengula"

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Earlier, journalists had been invited to apply to join one of these indaba groups. The Times asked to attend one yesterday but was refused – despite the session being entitled “Never say no to media”.

Some bishops opted out from the start, preferring to go shopping in Canterbury, but even among those prepared to give them a try, the muttering soon began. Indaba groups need time. Hours of it. This is not what the bishops at Lambeth have. They have clocks that have to be watched, meetings to get to, lunches to eat, sermons to preach and schisms to prevent. Indaba groups also need both sides in a dispute to be present: a quarter of Anglican bishops, overwhelmingly conservatives from the developing countries, have boycotted Lambeth.

Bishop Tilewa Johnson, from Gambia, said that his own villages used indaba, but called it bantaba, which means “under the big tree”.

“The fact that an attempt has been made to use the process is a good one. But of course it clashes with the culture here of everybody keeping an eye on the clock,” he said. “Indaba has no time limit. We keep going until a solution is found. Indaba takes place under a huge, shady tree where villagers assemble to talk about things. The aggrieved and the perpetrators must both be there to respond.”

Allison Lawrence, wife of the Bishop of South Carolina, Mark Lawrence, said: “They have taken a Zulu word and used it for an American concept. The African concept when you do an indaba is you talk, talk, talk until you agree. In these indaba groups, they talk a little and then someone changes the subject if they don’t like it. The Americans are feeling railroaded and manipulated. Even the Africans are saying, ‘This is not indaba’.”

Bishops emerging from yesterday’s sessions described being divided into groups of about 40. As if there were not already enough divisions among Anglicans, they were divided up further into groups of four or five and given papers on subjects that the conference is addressing: mission, millennium goals, poverty – the list is long. They talked and a rapporteur took notes, to be passed up to the next level. No one quite knew who or where that was.

Moreover, none of the bishops asked by The Times had yet been given a chance to discuss the one thing that they are all desperate to address: how can the Anglican Communion survive the consecration of Gene Robinson, the openly gay Bishop of New Hampshire.

The Archbishop of Sudan, Dr Daniel Deng, heightened tensions yesterday by saying that Bishop Robinson ought to step down.

One English bishop, limping down one of the long and winding concrete paths between the different indaba groups on the campus of Kent University, confessed that he was suffering from total exhaustion.

The Archbishop of Canterbury, he said, had been superb; the three-day retreat at the start of the conference drew everyone attending together; but something needed to be done about indaba, he confided.

“We have been given too many things to do and not enough time to do it. The proper indaba process works over a long period of time. It needs looking at rapidly. We need more space,” he said.