The Met Office said that with two bands of rain set to hit England and Wales in close succession, a yellow warning has been put in place until Wednesday.
The region will be waking up on Tuesday to “strengthening winds” and “everyone will have a windy day,” according to forecasters. Powerful 50-60mph gusts may hit Scotland’s west coast and Northern Ireland while exposed regions such as the outer Hebrides may have to contend with 70mph gales.
The Environment Agency warned that rivers and areas already hit by record river levels throughout the wettest December on record, including Cumbria, Lancashire and Yorkshire, may be deluged.
High spring tides combined with high winds could cause a flood risk along south-west and north-west coasts, and heavy rainfall brings a risk of river flooding in the north, Midlands and south west, according to the agency.
Communities in Cumbria, Lancashire, Yorkshire, the Midlands and the south west as well as central southern England are the main areas at risk.
The system is the “remnants” of Storm Jonas, which has battered the US East Coast killing 18 people.
A Met Office spokesman said: “There will be several low pressure systems which will work their way across the UK. The amounts of rainfall could be pretty high, there is potential for 50 to 100mm, which is four inches.
“Across northwest England and Scotland there could be upwards of 150mm, almost rivalling what we saw in December.
“These are quite wet areas and they are susceptible to flooding.”
Leeds and York were all hit by the severe weather, alongside scores of towns and villages, and thousands of residents had to be evacuated from their homes on Boxing Day.
Dozens of victims have been left homeless after rivers burst their banks and flood defences failed.
The Met Office said the warning could be extended to south-west and south-east England.
The Environment Agency said it is monitoring river levels and has warned residents to “be prepared for the possibility of flooding”.
“We will monitor rainfall closely and urge communities to be vigilant,” a spokesman said.
“With heavy rainfall predicted in those areas there is obviously a risk of flooding.
“We will have crews out in the next couple of days and if the river levels rise then we could issue warnings.”
Storm Jonas brought hurricane-force winds and up to 60 cms of snowfall to the East Coast of America, bringing many states to a standstill.
Inbound and outbound flights from major airports across America were cancelled, at least 45 of which were coming from or going to the UK.
A state of emergency was declared across a vast swathe of the eastern seaboard, with schools and government offices closed, sports and entertainment events called off and thousands of homes without power.