Large parts of Britain are facing days of disruption after one of the worst winter storms of recent times triggered an unprecedented number of flood warnings and left thousands of homes underwater.

Major incidents were declared in south Wales and parts of England as Storm Dennis brought heavy rain and strong winds to much of the country.

A man died after being pulled from a swollen river in the Swansea valley although police said the incident was not directly linked to the weather. Dyfed-Powys police said the man was seen entering the River Tawe and was rescued downstream but could not be saved by paramedics at the scene.

The north Atlantic storm, described as a “bomb cyclone”, triggered nearly 600 flood warnings and alerts in England alone on Sunday, more than any other day on record, with dozens more in place across Wales, Scotland and Northern Ireland.

In south Wales, police declared a “major incident” after more than a month’s rain fell in 48 hours, leading to multiple landslides and people being trapped in their homes. The local MP, Alex Davies-Jones, said she had been “truly heartbroken” to see the damage caused to more than 1,000 homes in the area.

The town centre of Pontypridd was underwater, with surrounding towns and villages told by the Met Office they could be cut off “perhaps for several days” because of the floods. Some 600 people were evacuated and placed in emergency accommodation overnight on Saturday.

Hundreds of flights were cancelled and roads and railways were submerged as George Eustice, the newly appointed environment secretary, said the damage left by Storm Dennis was expected to be worse than that caused by Storm Ciara last weekend.

He said officials did not expect to declare a national emergency but that they would monitor river levels in the coming days as the storm tracked north to Scotland and Northern Ireland. “It’s not a national emergency yet but it is certainly a local emergency in many of those areas affected,” he said.

Later, speaking during a visit to York to discuss tackling flooding, Eustice said the government had not been caught off guard by the storm. He told Sky News: “We can’t do anything about these extreme weather events but the steps we’ve taken have meant the impact of those weather events has affected fewer properties.”

He added: “We’ll never be able to protect every single household just because of the nature of climate change and the fact that 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.”

Homes were also flooded in Herefordshire and Worcestershire, where there were four severe flood warnings in place, meaning a danger to life. Sarah Bridge, 55, compared Storm Dennis to a tornado and said water had flooded her home in Pontrilas in Herefordshire despite specialist flood doors, reaching up to her knees. “It’s heartbreaking,” she told the BBC. “The kitchen is completely flooded, I can hear things floating about downstairs.”

In West Yorkshire, parts of the Calder valley that were badly hit last week breathed a sigh of relief on Sunday morning as river levels did not rise as high as feared. In Mytholmroyd, the River Calder rose to 2.8 metres overnight, just short of the three metres that would have topped the makeshift flood defences installed in recent days.

Soldiers from the 4th Battalion, Royal Regiment of Scotland, were drafted in to Calderdale and Ilkley on Saturday to protect residents against the expected deluge from Storm Dennis, and their efforts appeared to have paid off.

Calderdale council has asked the government to treat the weather as a national security threat akin to terrorism for its flood-prone valleys after it was hit by four floods in eight years.

The council’s chief executive, Robin Tuddenham, has written to the government asking for “tier one” status to make the region the highest priority for national security, putting the area on a similar footing to the City of London, which faces a terrorism threat.

About 170 flights were cancelled as of Sunday morning, affecting at least 25,000 passengers at airports from Edinburgh to Heathrow and Southend.

The Met Office said that winds of more than 80mph were recorded across parts of the country, with the highest measuring 91mph in Aberdaron in north Wales on Saturday.

A total of 156.2mm of rain fell at Crai Reservoir in Powys in the 48 hours from Friday to Sunday morning, compared with its average February rainfall of 111.1mm.

In Scotland, two people had to be rescued after their car was swept off the road by a torrent that pinned it to a metal gate near Newcastleton in the Scottish borders, where a number of flood alerts were in place.

The Forth and Tay road bridges were closed to all traffic on Sunday evening because of high winds.

The Scottish Environment Protection Agency’s (Sepa) highest warning level remained in force for Newcastleton and Hawick on Sunday after some residents were advised to leave their homes.

A search was under way after a woman was seen going into the water at the beach in Brighton. Police were called in the early hours of Sunday morning after emergency services carried out a search throughout the night.

A spokesman for Sussex police said: “At 0245 on Sunday, police received a report that a woman, believed to be in her early 20s, had been seen to enter the water from the beach at Brighton opposite Kings Road.

“She’s not so far been found despite an extensive search during the hours of darkness in both sea and on shore by emergency services including coastguard, Sussex police and Brighton beach patrol staff. The weather has been very bad, with rain and high winds. The circumstances are currently being treated as unexplained but not suspicious.”