As homes along the River Thames were evacuated yesterday and thousands more are at risk from rising water levels - with more wet weather due over the coming days - efforts to deal with the flooding have been overshadowed by the bitter clash.
It follows a barbed apology by Communities Secretary Eric Pickles on Sunday for relying on its advice.
Environment Secretary Owen Paterson, who was leading the response until being forced to undergo an eye operation, is said to have complained to Downing Street over Mr Pickles.
Both ministers have played down the apparent rift, insisting they are "working closely" to respond to the crisis.
But furious Environment Agency chairman Lord Smith hit back, saying his staff know "100 times more" than any politician about flooding. He also squarely blamed Treasury funding rules for the failure to dredge rivers.
Attempting to take the heat out of the spat yesterday, the Prime Minister said: "I am only interested in one thing, an that is making sure that everything government can do is being done, and will go on being done to help people through this difficult time.
"This is a time for everyone to get on with the jobs that they have.
"This is not the time to change personnel here. This is the time to get on, do everything we can. I back the EA, I back the work they are doing.
"There will be time later on to talk about things. Right now everybody's got to focus on the job in hand. That is the EA, every department in government, and let's not forget the emergency services and the army, who are doing a brilliant job."
Number 10 rejected suggestions that the Cabinet was at war, with the Prime Minister's spokesman saying: "I don't think there is a difference between Eric Pickles and Owen Paterson on this."
Asked whether Mr Cameron agreed with an unnamed Cabinet minister quoted as saying Mr Paterson was "stupid", Mr Cameron's spokesman said: "The Prime Minister's view is that Owen Paterson does an excellent job."
He denied that there had been a lack of urgency in the Government's response during the early stages of the flooding, when the emergency Cobra committee was sometimes chaired by a junior environment minister.
The spokesman said Mr Cameron associated himself with the "unreserved apology" offered by Mr Pickles, who accepted that it was a mistake to have stopped dredging Somerset Levels rivers.
"The Prime Minister would associate himself entirely with Eric Pickles's apology and the reason why, which is that there hasn't been the dredging that was required and that is something that is going to be put right," said the spokesman.
Mr Pickles told MPs there was a "marvellous workforce" at the agency and told the Opposition to stop trying to score "political points." Mr Pickles chaired a Cobra meeting in London last night with the Prime Minister participating by phone.
Labour leader Ed Miliband said: "It is a disgrace that you have Government ministers pointing the finger at each other when they should be rolling their sleeves up and helping those affected."
Strong winds expected mid- week could add to the problems facing areas which have seen severe flooding particularly in the Somerset Levels. Last night there were 14 severe flood warnings in place in Berkshire, and Surrey, while two remained in Somerset.