Yorkshire Water has brought in extra staff to deal with an "unprecedented" number of calls about frozen and burst pipes.
The firm said it was currently receiving up to 8,000 calls a day. On 22 December it took 10,000 calls.
The Malton and Haxby areas of North Yorkshire are among the worst affected, with some people saying they have been without water for over a week.
Yorkshire Water said it was doing everything it could to help customers.
One woman, Yvonne Sturdy, 67, from Malton, told BBC Radio York she had been without water for 11 days, and her heating had now gone off.
"You don't realise how precious water is," she said.
Mrs Sturdy said her neighbours had been helping her by bringing her water.
She added that she had been told by Yorkshire Water that she would have to wait until the frozen pipes thawed out.
Richard Sears, from Yorkshire Water, said: "In a normal day we would usually have around 1,000 calls from customers. On a daily basis we are now getting 8,000 calls a day, which is very testing."
He added: "We have drafted in extra staff. Unfortunately this did happen over the Christmas period."
He added they had embarked on a huge media campaign over the past few weeks on how customers could get help, but many of the calls were related to issues that were not in their power to deal with.
"We are only responsible up to the boundary of the property.
"Where possible we have helped customers."
He added that staff had gone out of their way to deliver bottled water to vulnerable customers, who were the company's priority.