According to Chief Constable Craig Mackey, of Cumbria Police, it could take years for Cumbria to recover from the damage.
He said: "We will be working with our communities for weeks, months, and in some cases years to come.
"The particular issue which made this so different is the damage to infrastructures.
"It is highly unusual to see that level of damage to infrastructures and clearly means that this next phase that we are moving into as a county is going to take a considerable amount of time."
Jill Stannard, the chief executive of Cumbria County Council - who only took up her post last Thursday - said the damage from the floods had run into "tens of millions of pounds" after more then 1,300 homes were flooded by record daily rainfall last Thursday and Friday.
She said she had been in talks with central government departments over the weekend to seek financial support to deal with the aftermath.
Ms Stannard told the BBC Radio 4 Today programme the authorities were trying to establish the whereabouts of "less than 50" people who remain unaccounted for, although she stressed that many of these may have gone to stay with relatives and friends outside the area.
She acknowledged that many local people were "very frightened" about access to healthcare, but urged them to listen to official advice transmitted by the media rather than giving credence to rumours about the situation.
Anyone calling their GP will be able to get through, and the authorities are able to deliver prescriptions to everyone in Cumbria, she said.
"We are confident we can reach everyone," she said. "We have been reaching people over the weekend. People get very frightened - totally understandably because this is very traumatic.
"It is important that people listen to advice through the media and don't listen to rumour and gossip."