A spokeswoman said they were doing "all we can to get as many customers back on supply as soon as possible" and apologised "sincerely to those without water or with low pressure".
A Tweet from the water supplier said: "We're sorry to customers in Ashford Lenham who are waking up to no water this morning".
Thousands of properties across the United Kingdom are still without water after a rapid thaw caused pipes to burst.
The county's supplier, Southern Water, is one of four companies in the United Kingdom to issue the warning, following last week's snow and ice cold weather.
A lorry arrived in Rotherfield and South East Water workers unloaded huge supplies of bottled water for distribution among residents.
Some schools in the capital have said they will be closed on Monday because they can not guarantee running water.
The firms said they were putting as much extra water as they could into local networks and were fixing leaks and bursts as quickly as possible. No water on either site means we can't open the school.More news: BJP, Cong reach 'kingmaker' UDP HQ at same time for Meghalaya support
Hundreds of customers took to Twitter to highlight problems with their water supply.
Four companies - Thames Water, South East Water, Southern Water and Affinity Water - urged customers who do have running water only to use it where essential.
Debbie Morrison told the BBC her house in Wandsworth had been without water since 20:00 GMT on Saturday "with no information on when the supplies will be reinstated".
Others have rallied to help their neighbours, offering to collect water for elderly or disabled people.
Schools in Derbyshire have been closed and homeowners across the East Midlands have been without water after freezing weather temperatures caused an "unprecedented" number of burst water pipes.
"We're asking customers to look at their pipes in their properties and end any unnecessary use of water, such as washing a vehicle", Mr White said.