Their criticism - plus an embarrassing contradiction over weapons of mass destruction by the US administrator of Iraq at the weekend - comes at the end of a miserable year for Blair whose popularity has tumbled over the invasion of Iraq.
The Archbishop of York, David Hope, who is the Church of England's second most senior churchman, said Blair had displayed "a real lack of listening" over Iraq and his claims of fallen dictator Saddam Hussein's arms capability remained unproven.
"Undoubtedly a very wicked leader has been removed, but there are wicked leaders in other parts of the world," he added in an interview with The Times newspaper.
Hope urged British churchgoers to pray for Blair, and said he and Bush should remember they will one day answer to God.
"I want to say...that there is a higher authority before whom one day we all have to give an account," he said.
The Bishop of Durham, Tom Wright, was scathing about Blair's military alliance with Bush in Iraq. He likened them to a pair of mavericks fighting crime in multi-racial inner-city London.
"For Bush and Blair to go into Iraq together was like a bunch of white vigilantes going into Brixton to stop drug-dealing. This is not to deny there's a problem to be sorted, just that they are not credible people to deal with it," he told The Independent newspaper.
"Strange distortion of Christianity"
"The world now needs a UN army in the way that Britain 200 years ago needed to turn its bands of militia in each town into a national police force."
Wright said the religious conservatives surrounding Bush espouse "a very strange distortion of Christianity" while the fact "some of them stand to benefit financially from the reconstruction of Iraq" made their motives suspicious.
Religious conservatives surrounding Bush espouse "a very strange distortion of Christianity"
Bishop of Durham
Blair braved major opposition in Britain before the March invasion, saw support rise as fighting began, but has since faced a barrage of criticism over the reasons for war and the
handling of post-Saddam Iraq. He has said he would do it again and is "ready to meet my maker".
Before Christmas, Blair told troops that the Iraq Survey Group hunting for banned weapons had found "massive evidence of a huge system of clandestine laboratories". But embarrassingly for the British government, Paul Bremer, the United States' top man in Iraq, flatly contradicted that as "a red herring" on Sunday.
The existence, or otherwise, of chemical and biological weapons in Iraq remains a huge issue for Blair - despite Saddam's capture earlier this month - because of the emphasis London put on that as a justification for war.
A weekend survey labelled Blair
Britain's least trustworthy politician
A weekend survey labelled Blair Britain's least trustworthy politician.
Former Cabinet minister Robin Cook, who resigned over the war, added to the chorus of criticism on Monday, saying London and Washington had opened the door to terror groups in Iraq.
"Far from being a victory in the war on terrorism, the invasion of Iraq has been a spectacular own goal, as our intelligence services accurately warned," he said.