One of the country's biggest power distributors has promised to almost triple compensation for people affected by long-term power cuts following the Christmas storms which swept Britain.
UK Power Networks, which owns electricity lines and cables in London, the South East and east of England, said it will increase payments from £27 to £75 as "a gesture of goodwill", with more than 1,700 homes in Kent, Surrey and Sussex still without electricity last night.
When the high winds struck on Thursday, power was initially interrupted to more than 300,000 customers, the company said.
Director of customer services Matt Rudling said: "This is such a difficult time of year for people to be without power and so many families have also been flooded out of their homes.
"Our hearts go out to our customers and we have been trying different ways to help them, from arranging Christmas dinners to providing more help and tools on our website."
A spokesman added: "As a gesture of goodwill UK Power Networks has decided to boost the industry standard payment from £27 to £75 for customers who are without power for 48-60 hours including Christmas Day, and additional payments will be made to any customers off supply for longer up to a maximum of £432."
The Energy Networks Association (ENA) said around 4,000 properties across the UK were still without power today.
An ENA spokesman said most of the south-east of England had been reconnected, except for " a few pockets where the damage was severe", while areas of Cumbria, North Wales and Cheshire were also affected.
Forecasters have said mild, wet and blustery weather will be a respite compared to the two major storms endured over Christmas.
Meteogroup forecaster Sean Penston said showers will mainly affect western and southern England, Wales and parts of Scotland before a light storm moves in tomorrow.
"It won't be nearly as bad compared to the last two storms but it will no doubt make it hard for people recovering from flooding," he said.
Some 105 flood alerts and 33 more serious flood warnings remained in place across the country this morning, the Environment Agency said.
In the south-east of England, Prime Minister David Cameron was confronted yesterday by an angry flood victim as he visited a village seriously affected by the latest storms.
The woman, named in reports as Ericka Olivares, said her local council had done nothing to help villagers in Yalding, Kent, where homes had been severely damaged.
In a heated on-camera exchange with the PM, she said: "We still have no electric. We need electric. As I say the council, from Monday we have been trying to contact them, but they have all decided to go on their holidays. Nothing."
The authorities' efforts to deal with the chaos caused by the first storm on Monday were hampered by the arrival of a second storm on Boxing Day night, bringing with it gales of more than 100mph.
More than 1,200 homes flooded, while many rivers burst their banks and groundwater flooding made roads impassable.
Kent County Council leader Paul Carter said better flood defences were needed to protect the area.
Speaking in Yalding, one of the worst affected areas, he told BBC Breakfast: "It would be nice to have extra money from central government to build some proper flood defences for this part of the country and the county of Kent.
"This area here in Yalding is very prone to flooding. This is certainly the worst flood that's been in this area for some 30 to 40 years but it does happen far too frequently.
"The big issue is there needs to be better flood defences built for this part of the Medway river because it's prone to flooding. I think everybody has done everything that they possibly could do to help and support the residents."
Despite the criticism from residents, Mr Carter said he believed the emergency planning operation in Kent had worked "exceptionally well".
He told the BBC Radio 4 Today programme: "Generally, the whole of the emergency planning operation has worked exceptionally well, in my view, over the last three or four days."
Robin Gisby, managing director of network operations at Network Rail, said this week "has been one of the most challenging periods we have faced in recent times".
Thursday night's storms meant that several trains were delayed yesterday morning so lines could be examined in daylight before trains set off.
The line from London to Portsmouth via Haslemere is blocked by four landslips near Liphook, and will stay closed over the weekend.
The track at Ockley between Horsham and Dorking is also closed following a serious landslip.
North West Ambulance Service (NWAS) took to Twitter to warn people about going outside in the gales.
A spokeswoman said the service had taken half a dozen calls in Lancashire alone about people being blown over by the wind, though only minor injuries were reported.
NWAS said that, as a precaution, people should stay indoors, out of the windy weather.
Conservative MP for Hastings and Rye Amber Rudd criticised Southeastern trains for failing to provide a replacement bus service for her constituents in the commuter belt towns.
While Southern Rail was offering workers the option of commuting to London via bus and even using Twitter to post regular updates, Southeastern services, including their communications, had been "lamentable", she said.
"So Southern have really done very well," said Ms Rudd. "I think it's partly because they've got Gatwick Airport on their tail wanting a better service.
"But Southeastern has not been anywhere near as good, and I have received a lot of complaints about them. They have been just too complacent".
UK Power Networks said 663 customers in Kent, 97 in Surrey and 326 in Sussex remained without power today.
A spokesman said: "Due to the severity of the storm damage it may take until the end of the week to restore power supplies to the final single premises affected in these areas, though work is continuing to reconnect most of the remaining supplies as quickly as possible."
Electricity North West (ENW) said 1,600 customers were still without power in Cumbria today after engineers restored more than 20,000 properties across the region.
At the peak of the storm on Thursday night, 15,000 properties were without power, while a total of 24,000 properties have been affected, the company said.
An ENW spokesman said: "The wind has blown trees and debris into overhead power lines and snapped electricity poles in a number of areas.
"Yesterday conditions made it difficult for engineers to access sites due to trees blocking roads, and the wind also prevented linesmen in some areas from climbing poles to restore supplies.
"We've drafted in extra engineers to help clear the trees and debris to ensure we restore power as soon as possible."
In Wales, around 1,500 properties - mainly in Anglesey and Gwynedd - were still without power this morning, a spokesman for Scottish Power said.
Despite forecasters predicting a weekend of more settled weather, the Met Office has issued a yellow warning - meaning be aware - for the early hours of Monday morning.
Heavy rain is expected to spread across the south west of England and south Wales on Sunday night into Monday morning, the Met Office said.
Winds of 60-70mph are expected to hit Wales and parts of south-west and southern England, while exposed areas such as the Isles of Scilly, west Cornwall and west Wales could see gales of up to 80mph.
"With ground already saturated over much of this region, the public should be aware of the risk of further local flooding," the Met Office said.
Scotland is also braced for more heavy rain overnight on Sunday into Monday morning, with 20-30mm of rainfall predicted and much as 50-60mm over high ground.