Parts of the UK were buffeted with winds of more than 90mph while more than a month's worth of rain fell in 48 hours, leading to to a record number of flood warnings and alerts in England.
But as Storm Dennis begins to move away, experts have warned that the UK still faces wet and windy weather and flooding.
The Environment Agency (EA) urged people to remain vigilant and said "significant" river and surface water flooding is expected to continue into next week.
Flood duty manager Caroline Douglass added: "Storm Dennis will continue to bring disruptive weather into early next week, and there are flood warnings in place across much of England.
"We urge people to check the flood risk in their area and remain vigilant."
Roads and railways were flooded on Sunday morning after torrential downpours and high winds caused by the second storm in just over a week.
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 until 11am.
EA's flood and coastal risk management executive director John Curtin said that there were a record number of flood warnings and alerts in force.
The EA said on Sunday afternoon that there had been more than 600 flood warnings and flood alerts in place across England - covering an area from Scotland's River Tweed to the rivers of west Cornwall.
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, it added.
The average monthly rainfall for February in Wales is 111.1mm, the Met Office added.
But Meteorologist Craig Snell said that while Storm Dennis was moving away from the UK, wet and windy weather would continue - with scattered showers and winds of around 50mph to 60mph.
He added: "We are not out of the woods yet with wind.
"We have got to get all this water through the river system so even though the warnings from us may expire flood warnings are likely to remain in force for the next 24 hours."
Yellow weather warnings for wind are in place on Monday, while an Amber warning for rain is due to expire at 6pm on Sunday.
Severe flood warnings have been issued for the rivers Neath and Taff in South Wales, as well as the River Teme further north.
Pictures on social media show the Taff bursting its banks and flooding parts of Pontypridd, while rescue workers were using boats to get families to safety after further flooding in nearby Nantgarw.
South Wales Police said it had declared a major incident due to the flooding and severe weather.
Streets have been evacuated with the help of a lifeboat in some of the worst-hit areas and people moved to emergency rescue centres after their properties and businesses were devastated by water from overflowing rivers.
One of the worst-hit areas in South Wales was the village of Nantgarw, Rhondda Cynon Taff, near Cardiff, which had seen entire streets left under water since the early hours of Sunday morning.
A man in his 60s died after being pulled from the River Tawe ear Trebanos Rugby Club, despite paramedics battling to save his life - police said he was pronounced dead at the scene.
Dyfed-Powys Police said that the man had been seen entering the River Tawe near Gorsedd Park in Ystradgynlais area, in South Wales, at about 10am on Sunday morning.
The force said the death was not being treated as suspicious or being linked to the bad weather.
Severe flood warnings were issued for the Scottish Borders, but these were no longer in force by late on Sunday morning.
Earlier, the Ministry of Defence deployed British Army personnel to assist people in West Yorkshire areas badly hit by flooding during last weekend's Storm Ciara.
Many flights have been grounded for safety reasons, with British Airways and easyJet confirming cancellations.
More than 230 easyJet flights in and out of the UK on Saturday were cancelled, while several sporting fixtures were also called off due to the weather.
Two bodies were pulled from rough seas on Saturday, before the worst of the storm hit.
One man was found following a huge search operation off Margate after an early-morning distress call, while another was found at Herne Bay.