South East Water says it is confident of returning supplies by Christmas
A water company boss says he is "very confident" that supplies in parts of Kent and Sussex will be back to normal by Christmas.
Southern Water said a burst pipe in Broadstairs had been fixed, meaning all customers were back in supply.
Meanwhile, South East Water said tap water was returning across Sussex and Kent, but customers in Tunbridge Wells still had an intermittent supply.
Both firms have apologised.
Areas still affected include Crowborough, Crawley Down, Mayfield, Stonebridge, Balcombe, Ardingly, Turners Hill and Tenterden.
South East Water's chief executive David Hinton told BBC South East Today: "We're very confident we can get customers on before Christmas, we think that's really important.
"All the treatment works that were affected are all now back in operation.
"We're very conscious of Christmas so we're trying to get the water supply back on before then and make it sustainable."
He said about 5,000 properties were still affected on Wednesday, but he hoped most would be reconnected by Thursday morning.
Bottled water stations were operating at Beacon Academy in Crowborough and Tesco in Pembury.
Southern Water said as water starts to return, customers may still have low pressure.
"This is normal and is only temporary. You can also expect to see bubbles and discolouration," a spokesperson said.
"We are so sorry for the distress this incident has caused."
Supplies returned to Cuckfield overnight, South East Water said, with teams working to reconnect further properties elsewhere.
Customers in Selsfield, West Hoathly, Sharpthorne, Crawley Down and Crowborough will slowly start to see supplies return, South East Water said.
The firm said the rapid thaw of frozen pipes had increased the level of bursts and leaks on their underground network of pipes, causing their storage reservoir levels to drop.
"On a normal winter's day, we extract, treat and pump an average of 520 million litres of drinking water. During the past 24 hours, this has increased by 100 million litres to 620 million," a spokesperson said.
Follow BBC South East on Facebook, on Twitter, and on Instagram. Send your story ideas to [email protected].