Forecasters issued yellow alerts for heavy rain covering central and south-western Scotland and parts of Yorkshire across Friday and Saturday.
And the Environment Agency has warned of worsening conditions across the Pennines and Yorkshire in the aftermath of Storm Dennis.
Five severe flood warnings which pose a danger to life and less serious 75 flood warnings are in place.
Dan Suri, chief forecaster at the Met Office, said: “With further rain in the forecast over the coming days and the potential for another deep low-pressure system early next week, additional rainfall could create further challenges as river catchments are more likely to respond to extra rainfall more quickly.
“Flooding, especially in areas already heavily affected, remains a possibility.”
The weekend is expected to bring more wet weather, with the possibility of sleet and snow in Scotland.
London will experience rain over the weekend, with conditions set to brighten from Tuesday.
Honister Pass in Cumbria, one of the wettest areas of the UK annually, recorded 185mm of rain in 36 hours on Thursday while 72 mm was recorded in Shap, Cumbria.
Capel Curig in Snowdonia, north Wales, recorded 86mm of rain in 36 hours after setting Wednesday's record for rain with 80mm in a single day.
Northern parts of England could see winds up to 65 mph on Friday, which could cause transport delays and adverse driving conditions.
The Met Office said Yorkshire is one of the most sensitive areas to rain at the moment, with only small amounts of rain potentially causing further flooding.
Forecaster Craig Snell said: "Rainfall amounts tomorrow are not exactly too high but the warning is because the ground is so wet."
The northern county is expected to see 20 to 30mm of rain falling, which could increase to 60 to 80mm in some areas.
"Given the recent wet conditions, even that amount of rainfall may cause some further flooding to occur," Mr Snell added.
He added: "Saturday is going to be a day of sunshine and gusty showers, the showers wintry across the north, chiefly across the high ground and we could see a bit of wintriness at lower levels but nothing amounting to too much at the moment."
He said the Met Office is monitoring an area of low pressure approaching the UK which could bring another spell of strong winds to Scotland, northern Ireland and northern England.
"Combined with the wind we would see the risk of further heavy rainfall and also potentially some snow as well for Scotland," Mr Snell said.
Hundreds of people have been evacuated from their homes in the worst-affected areas following days of flooding in the wake of Storm Dennis.