The Met Office also issued two severe weather warnings, meaning danger to life, for rain in the two counties.
Several rivers have burst their banks, and homes in Ribchester and Whalley, Lancashire, have been evacuated.
Meanwhile, more than 300 flood alerts and warnings are in place across England, Scotland and Wales.
Almost a month's rainfall is likely to fall in one day in some places. The Environment Agency said affected residents should "take action now".
Lancashire's severe flood warnings - meaning flooding is expected and there is a danger to life - are for two locations on the River Ribble at Ribchester, three on the River Calder at Whalley, as well as for the River Wyre at St Michael's North and St Michael's South.
The five Yorkshire flood warnings are around the Calder Valley area, with the River Calder, River Ryburn, Cragg Brook, Hebden Water and Walsden Water affected.
In other developments:
- More than 200 flood warnings, meaning flooding is expected, and more than 120 flood alerts, meaning flooding is possible, have been issued for England and Wales
- Several rivers have overflowed their banks, including the River Calder and the Rochdale Canal, leaving houses and a bowling club under water
- River levels in some areas reached record levels, according to the Environment Agency
- Flooding has brought travel "chaos" to roads in north Wales, with people rescued from cars and vehicles left stranded
- An amber warning of rain has been issued for Denbighshire, Conwy and Gwynedd in north Wales
- 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
- Some Boxing Day football has been called off due to heavy rain, with matches between Blackburn and Middlesbrough, Wigan and Sheffield United and Bury and Barnsley affected
- Officials at Wetherby Racecourse have called off both days of their Christmas fixture, Saturday afternoon's meeting at Limerick has been abandoned and Chepstow's Welsh Grand National meeting was called off
- More than 11,000 homes are without power in Rochdale, Greater Manchester
- The annual 'Nippy Dipper' swim at Aberdeen beach was cancelled due to stormy weather
- 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
The two red Met Office warnings for rain have been issued for parts of Lancashire as well as for West Yorkshire and North Yorkshire.
They warn of "widespread flooding" leading to disruption, with possible danger to life.
The Army is helping with the response in several areas.
'Don't visit'
Those being evacuated from their homes on Boxing Day were told they could go to nearby Longridge Civic Hall.
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."
Agency 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."
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.

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