David Cameron defended the funding available for defences as he met people in York taking advantage of a brief respite from the weather to start cleaning up.
But gales and downpours are forecast to sweep back in from this evening, with Cumbria and southern and central Scotland most at risk of more disruption.
Most of the nine remaining “severe” flood warnings issued by the EA for England and Wales - meaning potential loss of life - are centred on York, which was inundated on Boxing Day.
The service company KPMG, which is working with organisations across the north as they respond to the flooding, said there was an initial estimate of the cost of the month’s events at up to £5.8 billion.
The Prime Minister met victims as well as those involved in the emergency response and insisted cash for defences was increasing.
He dismissed a complaint from the council leader in flood-hit Leeds the North was being neglected, claiming it got more per head than the South.
But he conceded the regularity with which homes were now being flooded made a review of what was being spent where a vital exercise.
The Government has ordered a major review of flood prevention strategy after the latest incident saw 500 troops deployed to help clean up after thousands were evacuated and many left without power.
EA deputy chief executive David Rooke said it would have to look at ways to flood-proof homes as well as traditional defences as the UK was “moving into a period of unknown extremes”.
“We will need to have that complete rethink and ... move from not just providing better defences - and we have a £2.3 billion programme to do that over the next six years - but looking at increasing resilience,” he told the BBC.
That would include solid floors, waterproof plaster, electrics moved up the walls and better early-warning systems, he suggested.
Mr Cameron said: “We need to sit down and look at what we are planning to build, what we are planning to spend and see if more can be done.
“You don’t just protect people, of course, through the flood defences, although they are important, and of course while some flood defences haven’t worked this time, many flood defences have worked and protected thousands of homes.”
He declined to comment on calls by the GMB union for a halt to staff reductions at the agency it says will undermine its ability to launch out-of-hours responses to floods.
Shadow chancellor John McDonnell called for an independent assessment of spending on flood defences.
“Serious concerns have been voiced today at the Government’s cuts in flood defence spending since 2010. David Cameron is in danger of losing the confidence of council leaders and local communities hit by the floods,” he said.
“In order to restore confidence in government action, I propose that a prompt independent assessment is made of the future flood defence investment programme, led by independent experts, including local council leaders drawn from the affected areas.
“As Labour has already said, it is becoming increasingly clear that we need a cross-party approach to identify the resources required for future flood defences. And we must ensure that any investment programme remains secure beyond the life of one parliament.”
Green Party leader Natalie Bennett said the PM’s response was “wholly inadequate” and showed he had not “ grasped the reality of the climate change we’re already experiencing”.
She joined Committee on Climate Change chairman Lord Deben in calling for urgent action to prevent housing being built in flood-risk areas.
The Met Office said rain overnight would be much lighter than the recent downpours but Storm Frank - the sixth of the season - would arrive by this evening.
It has issued amber warnings with up to 40mm of persistent rain expected widely across Northern Ireland, west and south-west Scotland, Wales and north-west England - flooded by Storm Desmond - by tomorrow.
Twice that is possible - 80mm - over high ground, with some exposed areas in south-west Scotland and Cumbria warned they could be hit by 100-150mm.
It said the conditions were “not unusual for this time of year” and comparable with the storms of the winter of 2013-14.
Met Office chief meteorologist Will Lang said: “Everyone should be aware of the potential for disruption in places from further flooding and the impacts of the gales to transport.”
Justin Balcombe, KPMG’S UK head of general insurance management consulting, said: “The scale of the flooding over the last few weeks has seen communities across large sections of northern England, Wales, Scotland and Ireland severely impacted.
“In 2007 when a similar pattern of flooding hit, total insured claims were £3.2bn, however, we consider that the actual financial impact far exceeded this. We are assessing this month’s events through a number of economic lenses, resulting in an initial total cost estimate of £5-£5.8bn.”
This broke down into costs to different sectors such as the insurance sector, businesses, individuals, communities and government.
Costs will include insured losses of up to £1.5bn - the estimated cost of claims to be made by insured homeowners and businesses.
Meanwhile, the cost of under insurance was likely to be £1bn. The limits on many insurance policies mean they are inadequate for covering the full loss. This is driven in part by homeowners still feeling the effects of the recession and reducing insurance premium spend and coverage.
In addition, given the post-Christmas timing, homeowners will have indirectly increased their contents values with presents and food, and while several policies provide for such an uplift, many do not.