The government is urging the insurance industry to deal with flood claims as quickly as possible.
As the prime minister unveiled a £10m fund to help businesses recover from floods, his spokesman confirmed No 10 would hold a meeting with insurers on Tuesday.
David Cameron is calling on the industry to offer more help to dry out the UK's 5,000-plus flooded properties.
The Met Office has a yellow "be aware" warning for rain in south-west England.
Sixteen severe flood warnings are also in place in southern England.
Cornwall, parts of Somerset and Devon have already seen bursts of rain on Monday, while around 600 people are still without power across southern England and parts of Wales after cuts last week.
The prime minister, who visited flood-hit parts of Worcestershire and Gloucestershire on Monday, will chair another meeting of the Cobra emergency committee later.
He said that while the government had increased spending on flood defences in the past, there were still lessons to be learned from the latest floods.
"There are always lessons to learn," Mr Cameron said.
"Always important after every flood to ask what other things could be done, what other things should be done, what other schemes should be looked at and we will make sure we learn all the lessons."
Meanwhile, members of his cabinet office will chair Tuesday's meeting with insurance representatives.
Mr Cameron's official spokesman said the insurance industry should do its best to maximise help to flood-hit victims, including the "speedy" processing of claims and the provision of dehumidifiers to dry properties out.
He declined to say whether the sector should be offering "premium holidays" to those who have been flooded.
Resources 'in place'
The Environment Agency has repeated warnings that flood waters could rise again in southern parts of England.
Katherine Evans, a flood risk manager at the agency, said this depended on how much more rain falls over the coming weeks.
She also described her earlier comments that the Environment Agency was "stretched" in coping with the floods as a "slip of the tongue".
"In terms of resources, with ourselves, the military and all the other multi-agencies, we certainly have the right resources in place," Ms Evans said.
Up to 20mm (0.8in) of rain is forecast in south-west England on Monday.
The BBC Weather Centre said this would not normally cause too many problems but the Met Office warning was in place because ground was already saturated. There are also concerns about south Wales.
As well as severe flood warnings, the Environment Agency has almost 300 less serious flood warnings and flood alerts in England and Wales.
However, the situation in the worst-hit areas of the Thames is expected to improve this week.
Tuesday should be brighter and drier, with temperatures higher than average for this time of year, said BBC Weather forecaster Matt Taylor.
Another area of low pressure looks set to arrive on Thursday and Friday, with stronger winds and more rain, but it is not expected to be as intense as last week.
The £10m Business Support Scheme will make funds available to small and medium-sized companies affected by storms.
Businesses are also being given extra time to file their accounts, without being penalised. A helpline is being launched and can be reached on 0300 456 3565.
Business secretary Vince Cable said: "It is vital that small businesses affected by the flooding get assistance as quickly as possible.
"We know the insurance companies are working to process claims as quickly as possible and we will inform local authorities of their allocations from the Business Support Scheme on Thursday to assist businesses with clean-up costs or help them to continue trading."
Business and enterprise minister Michael Fallon said: "The scheme we're announcing today is specifically designed to help the very smallest businesses - the local shops in the village, the local stores, the independents."
He told the BBC it would give them "some immediate help", adding each business would be able to apply for a grant of up to £2,500 to assist their recovery.
In other new developments:
- Half of the high-capacity pumps being used to shift flood water in Somerset are working again after being switched off because of riverbank damage
- Flooded signalling equipment has led to disruption for rail commuters travelling between Brighton and London
- The reopening of the South West's main rail link will be delayed by up to another two weeks after more storm damage at Dawlish in Devon
- A landmark tree in Powys has been felled by high winds that hit Wales last Wednesday. The Lonely Tree, which stood on Green Hall Hill near Llanfyllin, had been regarded a landmark for more than 200 years