The government has pledged to help victims of widespread flooding across the UK, as gale force winds and torrential rain across a vast swath of the country claimed the lives of two people.

A 21-year-old woman was killed when a tree smashed into her tent while she was sleeping, near Exeter city centre, while a 70-year-old man died after his car crashed into a swollen river in Cambridgeshire.

The government said on Sunday morning that almost 500 homes and businesses had been flooded, mainly in the south-west of England and the Midlands. Overnight four severe flood warnings — meaning lives are in danger – were issued for Cornwall, though by first light this had been reduced to two. Dozens of sections of roads in the West Country, including the M5 and M50, were flooded.

David Cameron pledged that the government would do everything possible to assist the flood victims. In a tweet, he said: "Shocking scenes of flooding in Cornwall and around the country. Govt will help ensure everything is being done to help."

The tent tragedy in Exeter happened on Western Way shortly before midnight. The woman who died was trapped under the tree. Two men who were also believed to have been in the tent were injured. Police were investigating why the woman and her two friends were in the tent.

The 70-year-old motorist died when his car left the road near Earith, in Cambridgeshire. Passers-by pulled him from his vehicle and he was taken to hospital by air ambulance, but his life could not be saved. Conditions were described by locals as "pretty shocking" .

The RNLI's lifeboat crews were on standby to help in Exeter, and Helston and Polperro in Cornwall. Police warned people in flood-hit areas not to travel unless absolutely necessary and not to wade through contaminated floodwater. Meanwhile, landslips and flooded lines were causing delays and cancellations to train services in the south-west.

Emergency services also reported flooding from the river Avon in the historic town of Malmesbury, Wiltshire, where the water was 90cm (3ft) deep in places. A spokeswoman for Wiltshire fire and rescue service said: "It's been building up there for a few days and has flooded now in the area down by the river. Streets and houses have been flooded and we've rescued four people from two properties, three people from one house and a chap with asthma from another."

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."

There was a break in the weather in the south-west of England on Sunday morning but yet another band of wet weather was expected to bring in more rain later. The Met Office said the next few days were likely to remain unsettled and colder weather, perhaps even snow, predicted for next weekend.

Richard Benyon, the floods minister, said around 485 properties had been flooded and railway lines and roads were also affected. "We've had teams out right through the night trying to make sure we are co-ordinating work with the emergency services, with local authorities, resilience forums, communities, making sure the effect is being minimised," he added.

Benyon claimed 24,000 homes in the south-west had been protected by new flood defences. Speaking to the BBC, Benyon said: "That does show the importance of continuing to spend capital on flood defences." He claimed the country was in a "massively better" position compared with the great floods of 2007, that brought havoc to Gloucestershire and Worcestershire. However, it was clear that not all new defences were working. In the village of Kempsey in Worcestershire, where a number of homes were flooded, the Environment Agency was investigating reports that new pumps had failed.

By 9am on Sunday, as well as the two severe flood warnings for the day there were more than 250 flood warnings — where flooding is expected — in place. Eighty-nine of these were in the south-west and 80 in the Midlands. In addition more than 250 alerts — flooding possible — were issued.

Further west, rest centres were set up in parts of Cornwall as rivers burst their banks and residents were evacuated. More than 230 staff from Cornwall council were out working to help those hit by the flooding and the fire brigade said it had been the busiest night it could remember.

Among those evacuated were 10 people who had to flee the tiny community of Portholland, near Mevagissey in south Cornwall, after part of a cliff behind five houses collapsed. They spent the night in a hotel. Rescuers found time to save wildlife as well as humans, including young ducks being raised in a caged area on a river in the centre of Dawlish, cutting the cage open with bolt cutters to stop them drowning in the rising water.

Devon and Cornwall police's assistant chief constable, Sharon Taylor, who was co-ordinating the emergency response throughout the night, said the region was being buffeted by winds of up to 60mph and up to 60mm of rain. Taylor said: "Cornwall was hit in several places and we did have to have some partial evacuation and move people to recovery centres, but fortunately we have been able to move them all back, with the exception of a couple of elderly and vulnerable people who are being looked after overnight."

She warned people not to travel unless absolutely necessary, saying: "We have particularly found that people are still trying to get home and make their way to their properties, but of course some of this water is now contaminated with sewage, and of course that could cause people health problems if they continue to ignore the advice."

Eddy Carroll, the Met Office's chief forecaster, said: "The current very unsettled run of weather is set to continue with further spells of wet and windy weather expected across the country over the next few days. Further rain moving in from the west on Sunday continues the risk for further flooding and travel disruption.

"Along with the heavy rain, strong winds may add to the potential for travel disruption, especially across southern Britain. Winds gusting to 50 or 60mph are expected across southern counties of England."

The Met Office said it expected the weather to become drier and colder in most areas by the middle of next week.