Senior ministers have rallied round Gordon Brown after the ex-head of the civil service said the chancellor operates with "Stalinist ruthlessness".
Mr Brown is expected to be the next Labour leader
Lord Turnbull also told the Financial Times that Mr Brown had a "very cynical view of mankind and his colleagues".
He added that he would not allow "serious discussion" with colleagues.
But Mr Brown was defended by ministers and deputy leader hopefuls Hilary Benn, Alan Johnson and Harriet Harman, while Downing St criticised Lord Turnbull.
Tony Blair's spokesman said: "The prime minister made very clear yesterday his admiration for the chancellor's record as chancellor."
He added that it was "in the interests of good government that civil servants should not become the story".
Lord Turnbull, who was also Mr Brown's permanent secretary at the Treasury for four years, said of Mr Brown's discussions with Cabinet colleagues: "His view is that it is just not worth it and 'they will get what I decide'."
This strategy had enhanced Treasury control but had come "at the expense of any government cohesion and any assessment of strategy", he said.
"You can choose whether you are impressed or depressed by that, but you cannot help admire the sheer Stalinist ruthlessness of it all."
But Constitutional Affairs minister Harriet Harman defended Mr Brown, telling the BBC: "He is demanding of his colleagues, but he is demanding of himself because he wants to change things for the better."
"Not all civil servants admire strong political leadership."
International Development Secretary Hilary Benn said: "He is prepared to take tough decisions and I think we should welcome that in a chancellor and a future leader."
Lord Turnbull has criticised civil servants who broke confidences
And Education Secretary Alan Johnson, who is also aiming to run for the deputy leadership, added that Mr Brown had a "strong personality" and "knows his stuff".
But he added: ""The idea that ... he goes round and tells other ministers what to do, let me tell you, I'm the secretary of state for education, nobody comes and tells me what to do."
Lord Turnbull's comments, unprecedentedly outspoken for such a senior civil servant, came the day before what is expected to be Mr Brown's final Budget before succeeding Tony Blair as prime minister.
Lord Turnbull declined to discuss his comments on BBC Radio 4's Today programme because he thought he had done "enough damage already".
In the past Lord Turnbull has been highly critical of civil servants who broke confidences, telling MPs in 2005 that "derogatory comments in relation to elected politicians" could do "concrete" damage.
BBC political editor Nick Robinson said he had been told that Lord Turnbull thought he was talking off the record during his conversation with the FT.
Former Conservative defence secretary Michael Portillo said Mr Brown's "personality and qualities have led him (Lord Turnbull) to be outraged".
He added: "He's (Lord Turnbull) a bit of a stickler for convention and doesn't like things done in a rude way and perhaps he thinks Gordon Brown does things in these ways."
Liberal Democrat Treasury spokesman Vince Cable said the peer's comments confirmed what his party had been saying for a "long time" about Mr Brown.
"There is excessive micromanagement, with far too many decisions being taken in the Treasury by bright young things who have no feel for the practical problems on the ground," he added.
Mr Brown, who is the overwhelming favourite to take over as prime minister when Tony Blair steps down this summer, has faced previous attacks over his style, with some Blairites like Charles Clarke insisting he had to be more inclusive. Sir Stephen Wall, Mr Blair's former Europe adviser, said Mr Brown's period in charge of the Treasury had been characterised by a failure to communicate openly with other departments.
He told BBC News 24: "I think the issue here is: Is Gordon Brown capable of operating with the trust and transparency that is necessary for good Cabinet government?
"That has not been the way he has operated at the Treasury."