Damage has included the destruction of a former pub in Greater Manchester, and a large hole has appeared in the M62.
The Met Office has issued two severe weather warnings, meaning danger to life, for further rainfall.
More than 300 flood alerts and warnings – 22 of them severe – are in place across England, Scotland and Wales.
The Met Office said the heaviest rain was expected on Saturday morning, with rainfall easing in the afternoon.
But it added: “A further spell of heavy rain is then likely this evening before a clearance takes place from the northwest.”
The two red Met Office warnings for rain have been issued for parts of Lancashire and Yorkshire
There are seven severe flood warnings in Lancashire – meaning flooding is expected and there is a danger to life – and 15 in Yorkshire
Houses in Mytholmroyd, West Yorkshire, and in Ribchester and Whalley, Lancashire, were evacuated after rivers burst their banks
Soldiers, who were deployed to Cumbria on Christmas Eve, have been helping residents in Lancashire
Several rivers have overflowed their banks, including the River Calder and the Rochdale Canal, leaving houses and a bowling club flooded
Every river in Lancashire exceeded record levels, the Environment Agency said
Parts of Rochdale, Greater Manchester, flooded after the River Roch burst its banks
The M62 is closed westbound between junction 20 at Rochdale and junction 19 at Middleton after a large hole appeared in the carriageway as result of rain, with traffic being diverted
A 200-year-old former pub was destroyed by flooding at Summerseat, Greater Manchester
The Scottish Environment Protection Agency has issued more than 10 flood warnings, in the Scottish borders and Tayside areas, as well as a number of flood alerts
Emergency services including Lancashire Fire and Rescue Service and North Wales Police are warning motorists not to drive unless they need to, with some roads closed
Irwell flooded in the centre of Manchester near
Lancashire Fire and Rescue Service tweeted: “A severe flood warning means danger to life. It doesn’t mean ‘come and have a look’! Please don’t come to visit Whalley or Ribchester now.”
Ribchester resident Alan Tomlinson told the BBC the situation was “pretty grim” with many homes at risk of flooding.
“The village is under siege really,” he said. “The routes to the south are cut off and the route to the north, to Longridge, is under threat.”
Kellie Hughes, a hairdresser who lives in Whalley, said the situation was “a million times worse” than a fortnight ago when floods also hit.
She said: “It’s just horrific, really bad. I’ve got the sandbags down here and just doing the best I possibly can.
“There are no more sandbags anywhere. People are panicking. That’s my business and my home, it’s a double whammy.”
The government’s emergency committee Cobra has met again. Environment Secretary Elizabeth Truss said the priority “continues to be protecting lives, protecting homes and protecting businesses”.
Local Government Association environment spokesman, Peter Box, said councils were “pulling out all the stops” to find accommodation for those forced to leave their homes amid flooding.
“Storms in Cumbria and Lancashire have reminded us just how unforgiving and formidable nature can be but councils in the regions have worked hard to try and minimise the impact on residents,” he added.
“Plans have also been put in place to ensure that older and more vulnerable people are not put at risk and can still access the council help they rely upon.”
Flooding has brought travel “chaos” to roads in north Wales, with people rescued from cars and vehicles left stranded.
Capel Curig in north-west Wales had the most rainfall in the 24-hour period to 09:00 GMT Boxing Day, with a total of 168mm (6.6in).
Ben Lukey, of the Environment Agency, told BBC Breakfast: “We have been warning people to take action now to make sure that they keep themselves safe, to check out for vulnerable friends and relatives, to move valuable papers and other belongings to a safe place out of the way of water.”
Met Office forecasters said up to 120mm (5in) of rain could fall over the most exposed sites in northern England on Boxing Day – with the average rainfall for the whole of December in the North West being 145mm (6in).
Floods Minister Rory Stewart told BBC Radio 4’s Today programme: “As the rain falls, the rivers respond very quickly. Certainly what we’ve seen is rainfall levels that nobody’s ever seen before.”
People can access information from council websites and the Environment Agency Floodline.
The agency is also operating a phone line – 0345 988 1188 – which will be staffed rather than offering recorded information.
Live flood warnings from the Environment Agency and the Scottish Environment Protection Agency.