Senior judges have refused to back government plans to set up the new Ministry of Justice, it has emerged.
Lord Phillips is concerned about the independence of the judiciary
The Lord Chief Justice, Lord Phillips, told MPs it had proved impossible to reach a deal with ministers.
The judges fear their independence will be compromised as the Lord Chancellor takes responsibility for prisons and probation as well as courts.
However, the Lord Chancellor said judges and ministers were "extremely close" to reaching an agreement.
When asked by an all-party constitutional affairs select committee if ministers had a "constitutional crisis", he replied: "No, we have not. The point that has been reached is that parties are extremely close to an agreement.
"The discussions, as I understand it, still continue."
The government says it will push ahead with splitting of the Home Office in two - creating a new Ministry of Justice (MoJ) - even if it cannot get backing from senior judges.
Senior judges fear the new ministry, which took on responsibility for prisons, probation and sentencing policy from the Home Office on 9 May, will place less emphasis on the courts.
They are also concerned they will come under pressure to make decisions based on prisoner numbers and other non-judicial factors.
Lord Phillips said creating the MoJ - which he told MPs he first learned about in an article in the Sunday Telegraph newspaper - would cause a "serious constitutional problem", rather than a "crisis".
He wants an inquiry into the issues raised by the new ministry - and he called for "constitutional safeguards" to ensure the continued independence of the judiciary.
"We have now reached the firm view that there is a need to have a fundamental review of the position in light of the creation of the Ministry of Justice," he told the Constitutional Affairs Committee.
Lord Falconer had hoped to reach an agreement but he told the judges a number of topics were off limits, including the executive agency status of HM Courts Service and the possibility of ring-fencing its budget.
Lord Phillips told the committee: "We've tried very hard to reach an interim agreement to tide over the period that will elapse before a review, and any implementation of it can take effect."
He said the Lord Chancellor did not agree there was a need for a review.
"This has become a fundamental difference between us," he told the committee.
A particular sticking point was the executive agency status of the courts in England and Wales, he said.
The judiciary's chief negotiator on the working group Lord Justice Thomas said they wanted to secure a review of the current position, adding: "We wouldn't have thought it was an awful lot to ask."
Following the split, the Home Office will be left to concentrate on dealing with terrorism, security, immigration and policing.
The Conservatives have urged the government to sort out the situation.
Shadow constitutional affairs secretary Oliver Heald said: "This represents a very serious constitutional problem, and a situation which requires prime ministerial intervention, whether by Tony Blair or Gordon Brown.
"They should not be going on roadshows. They should be sorting out this serious issue."