Archbishop Orombi is boycotting the Lambeth Conference along with 200 other bishops in protest at the presence of liberal Americans and Canadians who elected an openly gay bishop and who have blessed same-sex unions in defiance of tradition.
He said: "The spiritual leadership of a global communion of independent and autonomous Provinces should not be reduced to one man appointed by a secular government."
Writing in The Times, he went on: "Even the Pope is elected by his peers. But what the Anglicans have is a man appointed by a secular government. Over the past five years we have come to see this as a remnant of British colonialism, and it is not serving us well."
His comments came as the bishops who arrived two weeks ago for the once-a-decade meeting finally began discussing the divisive issue of human sexuality.
Liberals and conservatives, who at the last Lambeth booed and hissed each other's speeches, were said to have held hands and embraced yesterday as they exchanged views and experiences of homosexuality, although none were reported to have changed their entrenched opinions.
A senior Vatican figure yesterday admitted that the liberal direction of the Anglican Communion has put an end to any hope of closer ties with the Roman Catholic Church.
Cardinal Walter Kasper told the 670 bishops gathered for the conference that the increasing number of churches that are ordaining women as bishops had changed the relationship between the denominations.
He said the modernising moves "effectively and definitively" blocked the recognition of Anglican holy orders as valid by Rome, more than a century after the then Pope declared them invalid.
Cardinal Kasper, the head of the Council for Christian Unity and the third senior Roman Catholic to speak at Lambeth, also repeated the church's belief that homosexuality is "disordered" and urged the Anglican bishops to make a "clear statement" on their view of it.
He said: "The ordination of women to the episcopate blocks substantially and finally a possible recognition of Anglican orders by the Catholic Church.
"We hope for the continuation of a theological dialogue between the Anglican Communion and the Catholic Church, but the latter development directly undermines our goal and alters the level of what we pursue in dialogue."
The veteran gay rights activist, Peter Tatchell, arrived at Lambeth with a 40ft banner reading: "Stop crucifying queers".
Mr Tatchell, who a decade ago invaded the pulpit at Canterbury Cathedral during the Easter sermon, set up his sign outside a sports hall on the University of Kent campus where the bishops were meeting, but stewards escorted them out of a side door to avoid a confrontation.
He said he was protesting against the "homophobic" stance of African church leaders and said it was "utterly shameful" that the Archbishop of Canterbury, Dr Rowan Williams, had not condemned them.
Mr Tatchell said: "The Lambeth Conference is putting unity before human rights. There's not much evidence at this conference of the Christian gospel of love and compassion."
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