About 17,000 homes have had their water supplies restored over the last 24 hours, and no homes supplied by South East Water should be without water, the company said.
Some areas may have low waster pressure or an intermittent supply, it said.
Some customers in Crawley were still experiencing problems with their supply, Southern Water said.
Bottled water collection points were in place in Crawley, Rotherfield, Crowborough, Wadhurst and Cuckfield.
Overnight about 2,000 homes in Rotherfield, Mayfield and Cousley Wood had been without water.
Douglas Whitfield, head of production at South East Water, said customers would be compensated.
At the peak of the problem, more than 25,000 properties were affected, with some having been without fresh water for five days.
The government has announced an urgent review into the way water companies have handled the freezing winter weather.
Environment minister Therese Coffey said regulator Ofwat would be encouraged to take action "to ensure water companies up their game".
She said the review would consider whether statutory compensation should be paid.