The Met Office has issued a series of yellow warnings for heavy rain covering Monday and Tuesday.
The first one is for central and southern parts of Northern Ireland, affecting areas including Enniskillen, Omagh and Newry.
It begins at midday on Monday and continues until 6pm.
Forecasters say torrential downpours are likely to cause disruption to public transport and flooding in places.
Journey times could be longer, bus and train services may be affected, and some homes and businesses could be flooded.
The second yellow warning for rain begins at 3pm on Monday and continues until midday on Tuesday.
This one affects the south west of England and areas further east, almost reaching Portsmouth and extending as far north as Oxford.
It covers Wales, too, except the north and the west coast.
There is a warning that some communities could be cut off by flooded roads, while power cuts are possible.
Tuesday brings two additional yellow warnings. One for rain covers the south of England, east of Oxford and Portsmouth, and also the whole of Kent.
That begins at midnight and runs until midday on Tuesday.
A yellow warning has also been issued for rain and wind for Northern Ireland, beginning at 2am on Tuesday and continuing until 9pm.
Met Office chief forecaster Steve Willington, said: “Unsettled conditions will continue through the week, with a combination of rain, brisk winds and some further hill snow, particularly in northern areas where colder air remains in place.
“While many areas will see typical late January conditions, there is enhanced potential for some impactful weather on Monday night into Tuesday.
“We encourage people to keep up to date with the latest forecasts and warnings as details evolve.”
Sky News weather producer Dr Chris England said said 30mm to 80mm of rainfall was expected in areas over the next few days.
Read more from Sky News:
US winter storm leaves 140,000 without power
‘Strong case’ for social media ban on children, home secretary says
Keep up with all the latest news from the UK and around the world by following Sky News
In Devon, meanwhile, part of a historic pier was washed away during Storm Ingrid.
Images showed Teignmouth Grand Pier, built in 1865, missing a huge chunk of its structure.
