In confidential letters sent to the Papal Nuncio, the bishops expressed their concerns that the Archbishop of Birmingham, Vincent Nichols, would be a divisive figure.
The archbishop has been widely tipped to succeed Cardinal Cormac Murphy-O'Connor, who is due to announce his retirement is due to be announced in April.
However, the bishops' intervention is likely to have undermined his chances of being approved by the Vatican.
Reports had suggested that the next Archbishop of Westminster would be unveiled last week, but it can be revealed that no announcement will be made before Easter.
Bishops in the Vatican are divided over the appointment and a low-ranking bishop is emerging as one of the most likely contenders.
One bishop said he had written to the nuncio to make clear his unease at Archbishop Nichols's attitude.
"I said that I was uncomfortable with someone who is clearly so ambitious," he said.
Another diocesan bishop revealed that he also had serious reservations over the character and style of Archbishop Nichols, despite acknowledging that he appears to be one of the outstanding candidates.
"The confidence he has in himself and in his views is not always shared by those around him," he said.
"He is very organised and knows how to run the bishops' conference, but his strong character can be too strong.
"We need collegiality and I'm afraid that with [Archbishop] Vincent I'm not sure we'd have that."
The bishop added: "He could do with learning a little humility."
One MP who also wrote to the nuncio, Archbishop Faustino Sainz Munoz, who is based in London as the Vatican's ambassador, said that they had stressed that they do not want the next Archbishop to be "a career churchman", a label that critics have levelled at Archbishop Nichols.
He was passed over by the Vatican last time around, largely because he was seen as too liberal, but has emerged as one of the Church's most impressive figures.
The archbishop has led successful campaigns forcing the BBC to withdraw the cartoon series Popetown and the Government to abandon its plans for a nonfaith quota of pupils for faith schools.
He was one of three names included on the terna - or shortlist - that was sent by the nuncio to the Vatican in mid-January.
The other two were the Archbishop of Cardiff, Peter Smith, who is believed to be the nuncio's preferred choice, and Bishop Malcolm McMahon of Nottingham, who Cardinal Murphy-O'Connor is understood to want as his successor.
Their names were submitted to the Congregation for Bishops, in Rome, which is responsible for recommending one of the names to Pope Benedict XVI.
Despite meeting last week for the third time to discuss the candidates to be the next Archbishop of Westminster, they failed to reach a consensus.
With opposition to Archbishop Nichols from his some of his colleagues, Archbishop Smith considered too liberal by many in the Vatican and questions asked of Bishop McMahon's doctrinal views, there is an increasing likelihood that an outsider could be appointed as the next Archbishop of Westminster.
According to a senior source in Rome, Bernard Longley, an auxiliary Bishop of Westminster, is emerging as the most likely alternative.
The bishop, who has a long track record of ecumenical and inter-faith work, is well-liked by his fellow bishops. More significantly, he is receiving strong support in the Vatican.
Another candidate highly regarded in Rome is Fr Alan White, who was until recently the head of the Dominican order in Britain.
He is understood to have gained admirers during his brief spell as the assistant to the order's Master General in Rome, but has a low-profile domestically and would come as a surprising choice.
Speculation over who is going to succeed Cardinal Murphy-O'Connor has been heightened in recent weeks with many Vatican observers baffled that an announcement is still to be made.
The Congregation for Bishops has only recently turned its attention to the Archbishopric of Westminster, however, having to first select new archbishops for the significant posts of Rio de Janeiro and New York.
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(Source: TTCUK)