Surrey County Council has declared a major incident as thousands of people are currently without water.
Thames Water has apologised, saying Shalford treatment works in Guildford had technical issues "caused by Storm Ciarán" and water would "only gradually return" throughout Monday.
Bottled water stations were set up in Artington Park and Ride in Old Portsmouth Road, Guildford and Godalming Crown Court car park, but the latter has now run out of supplies.
Thames Water said on X, formerly Twitter, at 19:30 GMT: "We've made progress fixing the supply issues but need to refill reservoirs. We're providing bottled water till 9pm and expect to do so again tomorrow."
A little earlier, Chancellor and South West Surrey MP Jeremy Hunt said on X that Thames Water CEO Alastair Cochran had told him water was "going into supply and will be ramping up production rates" over the next three hours.
"Still some risk but remains promising that a solution may be in sight," the chancellor added.
Earlier, he said that even if the supplier was successful, disruption would continue overnight and into Monday.
Water was getting to vulnerable communities and local hospitals, Mr Hunt said.
Waverley Borough Council leader Paul Follows said he believed between 5,000 and 10,000 homes were affected.
At 20:00 GMT, he said he expected many areas would still be without water on Monday morning, and schools and nurseries would get official guidance at 07:00 on Monday about whether to close. Water stations would reopen at 09:00 on Monday, he said.
Mr Hunt said earlier that 13,500 homes were off supply with a further 6,500 expected to be cut off shortly.
Thames Water has not confirmed either of these numbers.
More than 18,000 properties across Southampton and the New Forest also lost their supply on Thursday evening, and many of them are still without water.
As well as Godalming, residents in the nearby villages of Milford, Witley and Bramley reported outages.
Mr Hunt said the next question was the potential impact on schools on Monday, if the incident was not resolved.
"Also getting messages from pubs that have lost trade from closing on a busy day - big, big impact on many people," Mr Hunt added.
There are plans to restock the water station at Crown Court Car Park on Sunday evening and both stations will be open until 21:00 GMT.
Supermarkets said people were panic buying bottled water and Waitrose in Godalming said it had sold out.
As traffic in the town built up, Mr Follows urged people who did not need to go out and get bottled water to avoid doing so.
"Try and carpool so there is not excessive traffic," he said.
BBC reporter Julia Abbott said her husband queued for water for about an hour and was only given enough for one household, despite requesting water for elderly neighbours.
Ian Boardman, who was queuing for water, said he had not been given any information about when his supply would be back and would rather not be "saddled" with plastic bottles.
He said: "I don't really want a load of plastic going into my recycling bin."
Susan Carlin, also in the queue, said she noticed her water stopped about 16:45 on Saturday.
"I noticed I couldn't flush the loo then my daughter said there wasn't anything coming out of the kitchen taps," she said.