More than 300 flood warnings are still in place across the UK, including five severe warnings in England, which mean there is a danger to life.
Major incidents were declared in south Wales and parts of England on Sunday.
It comes as the government said it would not be able to protect all homes from flooding.
Travel continues to be disrupted, with A-roads closed in Staffordshire and Nottinghamshire in England, and Powys and Monmouthshire in Wales. Roads are also closed in parts of Scotland, including the M90 Friarton Bridge.
Train services are affected on lines run by CrossCountry, Great Western Railway, Merseyrail, Northern, South Western Railway, Transport for Wales and Scotrail.
New Environment Secretary George Eustice denied the government had been caught off guard by the floods, which come a week after the UK was hit by another major storm, Ciara.
Speaking during a visit to York to discuss how to tackle flooding, Mr Eustice told Sky News: “We’ve done a huge amount.
“We can’t do anything about these extreme weather events but the steps we’ve taken have meant the impact of those weather events have affected fewer properties.”
Mr Eustice blamed the “nature of climate change” for the scale of the damage, adding: “These weather events are becoming more extreme, but we’ve done everything that we can do with a significant sum of money, and there’s more to come.”
The government has activated an emergency funding scheme for areas affected by the flooding, which include parts of Nottinghamshire, Leicestershire, Derbyshire, Shropshire, Telford and Wrekin, Worcestershire and Herefordshire.
Under the Bellwin scheme, local authorities can apply for the government to reimburse non-insurable costs above a certain threshold, which has not been specified.
A record number of flood warnings and alerts were issued for England on Sunday, according to John Curtin, the Environment Agency’s head of floods and coastal management – reaching a combined total of 634 by 06:00 GMT on Monday.
There are also more than 60 flood warnings and alerts in Wales and more than 20 in Scotland.
On Sunday, major incidents were declared in south Wales and parts of England, as parts of the UK were buffeted by wind gusts of more than 90mph.
More than a month’s worth of rain fell in 48 hours in places.
The storm caused flights and train services to be cancelled and roads to be closed.
The Ministry of Defence deployed Army personnel to assist people in West Yorkshire areas badly hit by flooding during the previous weekend’s Storm Ciara.
In York, thousands of sandbags have been placed around vulnerable properties near the River Ouse, with the Environment Agency warning the river could come close to record water levels seen in 2000.
The situation was said to be “life-threatening” in south Wales, where the Met Office issued a red warning due to heavy rainfall and flooding risk.
Dramatic video footage emerged of a landslide tearing down a mountain in Tylorstown, Rhondda Cynon Taf, south Wales, on Sunday morning.
South Wales Police said emergency services were working with local organisations to ensure the safety of people in communities cut off by flooding, and to minimise damage and disruption.
Emergency centres were set up for those who have been displaced.
Severe flood warnings are in place for the River Teme in parts of Worcestershire, Herefordshire and Shropshire and the River Wye in Herefordshire.
A man was rescued from the Teme, close to Eastham Bridge in Worcestershire, and taken to hospital by ambulance, police said. But a search for a woman who went missing in floodwater in Worcestershire was called off until Monday.
In Herefordshire, the council said it was working with the emergency services, the Environment Agency and health partners to assist residents.
It urged people to avoid unnecessary travel and check on their neighbours, and said “rest centres” are being set up for those who need to be evacuated.
In Scotland, the Forth and Tay road bridges were closed to all traffic.
Winds battered most of Scotland on Sunday with a Met Office warning in place until 11:00 GMT on Monday.
It comes after Storm Ciara brought as much as 184mm of rain and gusts reaching 97mph last weekend.
The storm also caused hundreds of homes to be flooded and left more than 500,000 people without power.
Transport Secretary Grant Shapps told Sky News’s Sophy Ridge the government was stepping up its response to extreme weather conditions.
He said it had put £2.4bn into defences over a six-year spending period up until next year, and would allocate £4bn for the next six-year period.