Police in Scotland have appealed to drivers in the south of the country to make only essential journeys.
The Met Office said Dumfries and Galloway and the Borders region could see up to 75mm (3in) of rainfall during the day.
Network Rail has brought in divers to inspect a flooded railway line near Llanrwst in Conwy Valley, north Wales.
Arriva Trains Wales is running a replacement bus service on the route between Llandudno Junction and Blaenau Ffestiniog.
In Cumbria, there are long diversion routes in place in Workington and other towns.
The closure of Calva Bridge in Workington, which has been condemned to demolition, means people face a lengthy detour to get to the other side of the town.
If the bridge collapses, the local authority has said some 11,000 homes north of the river will lose their telephone connections.
The rail bridge remains intact and Network Rail has said it will build a temporary station on the north side of the River Derwent.
AT THE SCENE
By Tom Symonds, BBC News
It was the first day back at school after the floods for Jenson, Chance and Tyler Mitchell. They live in Workington's Northside - the north side of the river that is - which given the lack of bridges, means it is cut off from the town that local people are used to having on their doorstep.
Maria Mitchell's plan is to drive her children in the opposite direction to the station at Flimby and catch the train. After all, the railway bridge into Workington remains intact.
But the drive, the wait for the train, the journey itself and then the walk to school takes an hour. And if Maria wants to go home while the kids are at school she'll have to do the trip four times a day. The train itself is standing room only.
"I'll be crying by Friday because I can't do this. I'll have to home-school my kids or put them in another school. We need something done about it," says Maria
It will be built on waste land about 800m (0.5 miles) from the existing station, reconnecting the two halves of the town which have been cut off following flood damage to footbridges and road bridges in the area.
The two-platform station, linked by a footbridge, should be ready by the weekend.
Bus operator Stagecoach will provide 10 vehicles to take up to 350 children from Seaton, Flimby and Maryport to school in Workington on Wednesday.
A total of six bridges have collapsed in the county and a safety review of all 1,800 crossings is under way.
Flood support centres remain open in Cockermouth, Workington and Keswick, offering advice on housing, insurance and other issues.
Conservative leader David Cameron has visited Cockermouth where he met residents affected by the floods and spoke to fire crews involved in the rescue effort.
He said: "Everyone's got to make sure that when the waters recede and when the television cameras go home that people in Cumbria aren't forgotten and that we give real help and real money with so many of the issues that need to be dealt with."
In the Commons, Health Secretary Andy Burnham praised the work of NHS staff and pledged the government would provide any extra resources needed.
Hundreds of residents have now returned to their properties to begin a huge clean-up operation.
Cumbria Police casualty bureau: 0800 0560944 or 0207 1580010
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