The prime minister insisted the government was investing billions of pounds into flood defences, as hundreds of homes were being evacuated because of the danger to life.
A woman died in Derbyshire when she was apparently swept away by waters while hundreds more were forced to flee their homes.
The Environment Agency repeated warnings for people to stay away from swollen rivers, with residents describing the deluge as “almost biblical”.
Fire crews were called in to help guide people to safety while rail and road users were warned against travelling on certain routes.
Residents in Doncaster, South Yorkshire, were told to evacuate their homes immediately as the Environment Agency warned against flooding from the River Don.
Some areas were hit by mudslides after more than 80mm of rain fell on Thursday. The average monthly rainfall total for Yorkshire at this time of year is 89mm.
Kathleen Overton, from Toll Bar, South Yorkshire, said: “It was almost biblical, I would say. You were just looking out of your window in disbelief at how much of it was coming down.
“People’s cars were getting submerged in the water, gardens were ruined, you couldn’t drive anywhere. It was carnage.”
During a visit to Matlock in Derbyshire, when asked what the government was doing to support people during floods, Mr Johnson said: “We’ve got a huge programme of flood defences and flood preparation – there’s £2.6bn going into it and I think £50m has gone into Derbyshire alone.
“But in the end, you’ve got to face the reality that places like this are vulnerable to flooding – we’re going to see more of it.”
He added: “You cannot underestimate the psychological effect of flooding on people – it is a big, big blow.
“But we are seeing more and more serious flooding – perhaps because of building, almost certainly because of climate change – we need to prepare and we need to be investing in those defences and that’s what this government is doing.
“It’s a good time to do it. The cost of infrastructure borrowing is low – so let’s get it in now.”
Residents in one street in Doncaster were rescued from their homes by boats on Friday as waist-high water filled the street.
Lacey Hanrahan, 24, told how she and her baby had to be taken on a boat when water started coming into her home. She said: “It got to the point where I wasn’t able to walk out, so I was taken out on the boat. I just can’t believe how deep the water has got.”
South Yorkshire Fire and Rescue Service said it rescued more than 100 stranded people on Thursday night.
About 35 homes in Mansfield, Nottinghamshire, were evacuated after a mudslide caused when a quarry collapsed, while residents in 25 homes in Worksop were also ordered to escape because of the floods.
Rail operator Northern advised passengers not to travel, with services between Hull, Leeds, Lincoln and Manchester disrupted.
Footage of a woman on a mobility scooter braving the severe flooding in Sheffield as though nothing had happened went viral on social media.
Stephanie Jubb, who captured the video, said: “She didn’t even lift her legs up or anything.”
She said the moment illustrated “northern spirit”.
Away from Mr Johnson’s visit in Matlock, Beth Windle photographed ducks sitting on the arms of submerged benches and able to reach higher bushes.
“The flooding is the most severe that I’ve known it, in my 25 years living here,” she said.
In Lincoln, Chelsea Foster said she was shocked to see swans swim to the wall at the bottom of her garden from an overflowing River Witham.
Alex Burkill, a meteorologist with the Met Office, said: “Some places have seen a month’s worth of rain in one day. The rain is easing and moving south but obviously the impact of that will continue to be felt.”
Additional reporting by agencies
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