David Cameron promised to help communities in the south-west of England and the Midlands that have been devastated after more than a month's worth of rain fell within four days.

On Saturday night a 21-year-old woman, who is believed to have been homeless, died after the tent she was sleeping in was struck by a tree that fell in high winds near Exeter city centre. Police were trying to trace her next of kin and find out why she was sleeping in the tent. Two men were injured in the incident.

A 70-year-old man was killed when his car crashed into a swollen river near Earith, Cambridgeshire. Local people described the conditions as "pretty shocking" though police said the accident could not be directly linked to the weather.

Over the weekend police in Watford found the body of a 50-year-old man who apparently fell into a canal early on Saturday after friends lost him in fog. In Berkshire an elderly man feared drowned in the Thames last week remains missing.

Last week a driver died as his car was swept away by floodwater near Bristol.

By Sunday night one severe flood warning – meaning lives are at risk – remained in place for Helston, Cornwall. More than 200 flood warnings – flooding expected – were in force and almost 200 alerts – flooding possible – issued.

But the government and the Environment Agency said most new defences, many introduced since the great floods of 2007, were working well and had protected more than 24,000 homes across England and Wales.

They will be tested again in the coming days. More rain is expected for the south-west and the Midlands on Monday. The level of rivers such as the Severn is expected to rise as the rain that has fallen in the last few days works its way down.

Heavy rain is also predicted to hit north-east England, with places such as Middlesbrough, Hartlepool and North Yorkshire regarded as the most significant flood risks on Monday.

Towns and villages hit by floods included Kempsey, Worcestershire and Polperro, Cornwall.

In Kempsey there was a blow for the Environment Agency in the failure of one of two large pumps forming a £1m flood defence system that was launched this summer. Water from an overflowing brook poured into homes.

Michael Gill, who was out of his cottage for 18 months after the 2007 floods, said: "It's devastating. I've never known the water come up so quickly. The water went up three or four feet in a couple of hours."

By lunchtime the water had been pumped out but left soggy carpets and ruined belongings.

Jan Perry, the landlady of the Old Mill House pub, Polperro, said she had never known flooding like it. At the height on Saturday evening water was pouring through the ground floor .

Perry said she was insured but asked: "How much will that cost to renew now? This makes me angry, though, as we'd already been having discussions with the council and the Highways Agency about the problems with the drain in the street outside. As usual, it has to take something like this to get anyone to take proper notice."

Stephen Gilbert, the Lib Dem MP for St Austell and Newquay, Cornwall, said the government needed to make sure insurance companies were able to provide home and business owners with affordable cover.

"The last two days should be a wake-up call for a government that needs to grip this issue and do so quickly. We know flash flooding is increasing because of climate change and there's now little we can do to stop it, but the government must act to make sure people aren't left without insurance when the worst does happen."

Other places hit by the floods included Malmesbury, Wiltshire. Chris Harvey, watch manager at the town's fire station, said: "It's the worst flooding I can remember in the town, certainly worse than in 2007 when there were problems."

The Environment Agency produced a map showing the properties that its flood defences were protecting, including almost 2,000 in Gloucestershire and Worcestershire, which were the most badly hit by the floods five years ago and 6,000 in Cornwall.

It said the flooding had been created by the exceptional conditions. The Met Office said in parts of the south-west around 150mm of rain – more than an average November – had fallen since Thursday on to ground and into rivers already swollen by a miserable summer and autumn.

Cameron said in a tweet: "Shocking scenes of flooding in Cornwall and around the country. Govt will help ensure everything is being done to help."

Richard Benyon, the floods minister, said the success of many of the defences showed "the importance of continuing to spend capital on flood defences".

Emergency services carried out scores of rescues of people stranded in cars and homes. A one-year-old baby was plucked from a car in north Somerset.

Around 10 homes in Old Sodbury, south Gloucestershire, were evacuated following a landslip.

It was a miserable weekend for travellers with flooded tracks and roads making travel difficult on rail and road. In many areas police and travel companies urged people to stay at home if possible.

By midweek it is expected to become drier and colder – with the possibility of snow next weekend in some places.