Social care chiefs do not believe children's safety is assured within services provided by the Diocese of Chichester, letters have revealed.
BBC South East Today obtained copies of the letters from East Sussex County Council to the Archbishop of Canterbury under the Freedom of Information Act.
The correspondence called for the immediate suspension of the Bishop of Lewes, the Right Reverend Wallace Benn.
Neither the Church of England or Bishop Benn have commented.
Solicitors for Bishop Benn said the letters released contained significant inaccuracies.
But they said legal obligations prevented the Bishop of Lewes from using confidential information to correct the inaccuracies.
In their letters, social care chiefs stressed the fact the diocese was a major provider of services to children in East Sussex - in schools, church-related activities and youth work - making its safeguarding operation a concern of the county council.
On 16 May, Matt Dunkley, director of East Sussex County Council's children's services, and Cathie Pattison, independent chair of the Local Safeguarding Children's Board (LSCB), wrote to the Archbishop of Canterbury, Dr Rowan Williams.
In their letter, they said: "We do not believe current arrangements within the diocese can assure the safety of children."
"We remain convinced that insufficient attention is being paid to the ongoing and immediate safeguarding of children in Sussex."
And the correspondence also revealed calls had been made for more than three months, for the immediate suspension of Bishop Benn.
The letter said: "We have no confidence in the judgement and conduct of Bishop Benn, in relation to dealing with safeguarding issues, and believe it is appalling that the Church seems reluctant to take decisive and immediate action.
"Bishop Benn faces serious questions of, at best, his competence to ensure children are protected, and at worst, his gross negligence in the face of serious allegations against staff he was responsible for.
"His position as bishop is plainly untenable until these matters are fully investigated."
On 7 June, a letter from Lambeth Palace to Mr Dunkley said the Church understood their frustration at the apparent lack of progress or action, but had to follow the rule of law and be above any risk of legal challenge, which meant the work had to be careful and painstaking.
That letter said: "Any process of suspension involves us jumping through several hoops and we are by no means certain that the evidence for such a step will be sufficient.
"I would add that the Church is not like other organisations in terms of employment arrangements."
The letter also highlighted that the diocese had been subject to "one of the heaviest sanctions the Church can impose" - the visitation process.
Under the visitation process, the powers and authority of the Diocese of Chichester had been taken over by the Archbishop of Canterbury, it said.
The visitation also included an inquiry into the diocese's child protection policies and an interim report was published on 30 August, when the Archbishop of Canterbury apologised to abuse victims and confirmed there had been "many and longstanding" failures in implementing safeguarding policy.
He said the visitation would continue until uniformly better practice could be assured.
Mr Dunkley and Ms Pattison issued a statement which said the letters reflected their long-standing concerns and frustrations about the way Lambeth Palace was investigating the handling of safeguarding matters within the Chichester Diocese.
They said: "These concerns were shared by all members of the LSCB in East Sussex.
"The letters speak for themselves and while the language used in them reflects the fact that they were not intended for publication, it does accurately reflect our strength of feeling on these extremely serious issues."
They said they welcomed recommendations made in the visitation interim report that attempted to bring the Church's safeguarding procedures into line with all other organisations that worked with children.