The newly formed Ministry of Justice (MoJ) came into being today, led by Lord Falconer after his Department for Constitutional Affairs was expanded to become the new ministry.
The split is designed to give the Home Office more scope to deal with terrorism, while responsibility for probation, prisons and preventing re-offending has been transferred to the MoJ.
But Mr Cameron insisted at prime minister's questions that the "last thing a department in crisis needs is the huge distraction of a big reorganisation".
Mr Blair defended his position saying: "It is right to take the prisons and probation out of Home Office and into a new Ministry of Justice.
"And while [Mr Cameron] says the department has failed across the board, let me just point out that as opposed to the previous government where crime doubled, crime has been reduced under this government."
But Mr Cameron was unrelenting, insisting that, with Mr Blair "tomorrow…announcing his departure" it was the wrong time to make such a move.
"The government is now paralysed," he said.
"We've got a home secretary [John Reid] splitting his department but he's already resigned. We’ve got a foreign secretary [Margaret Beckett] negotiating a European treaty that she won't be around to ratify and we've got a prime minister who even after last week's drubbing simply doesn't understand that it's over."
He added: "This is a government of the living dead – why do we have to put up with even more paralysis?"
Mr Blair is widely expected to announce that he will resign as Labour leader at his Sedgefield constituency tomorrow after ten years as prime minister, with chancellor Gordon Brown set to succeed him.
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.