Heavy rain could bring more floods at the start of 2014, the Environment Agency (EA) has warned.
Counties at increased risk of flooding are Cornwall, Devon, Somerset, Dorset, Wiltshire, Hampshire, Gloucestershire, Berkshire, Sussex, Surrey, Kent and Cumbria.
Parts of western Scotland are also at risk.
The EA has 19 flood warnings in place in England and Wales, meaning flooding is expected, and 151 flood alerts, where flooding is possible.
The Met Office has said that as much as 40mm (1.6in) of rain could fall on higher ground or coastal areas, and there are likely to be gales of 50-60mph.
The latest bad weather is set to push in from the Atlantic, crossing the UK from west to east.
With the ground already saturated, some minor flooding is likely, the Met Office said.
Sky meteorologist Chris England said: "Heavy rain over central and southern England and Wales will add to the flood risk there, while there will be gales over southern and western coasts and hills.
"Thursday will bring a spell of mostly fine weather, with just the odd coastal shower, but the next storm system will bring rain into Cork and Kerry by dusk.
"That rain will push across all parts overnight, clearing eastern England on Friday morning, but gales or severe gales following will bring squally showers to most areas.
"It will stay unsettled with further rain and strong winds into next week."
Councils are preparing for the worst, with emergency accommodation lined up in case people are forced to leave their homes.
The Local Government Association is urging people to look on council websites to keep updated with information.
An EA spokeswoman said: "People travelling this week are reminded to check the latest flood updates ahead of making journeys and should not drive through dangerous floodwater."
To date, there have been 1,300 properties flooded across England.
Seven people were airlifted to safety on Monday after heavy rain caused flooding in Scotland.
The group, which included four children, were rescued from a farmhouse near Closeburn in Thornhill, Dumfries and Galloway, by a Royal Navy helicopter.
Rain forced families to be evacuated from dozens of homes and caused major road disruption.
Advice on what to do before, during and after flooding is available on the Environment Agency website or by calling Floodline on 0845 9881188.
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