Sam Bottomley, from SWW, said the effect on supplies was “unprecedented”, with damage to mains from fallen trees and every pumping station out of action from power cuts.
“We are suffering the same as everybody else with power supplies, and we are working closely with the National Grid,” he told BBC Radio Cornwall.
However, the utility said on Monday morning that its Wendron treatment works had come back into service despite ongoing power outages.
It added: “We’re still working hard to restore water to customers in Nancegullan, Carleen, and Mullion, and, if everything goes to plan today, we expect all customers to be back in supply by the end of the day.”
Bottled water stations have been set up at Old Flambards Car Park in Helston, open 24 hours; Mullion School on Meaver Road, open from 07:00 GMT to 22:00; and Folly Field Car Park, Marazion, also open from 07:00 to 22:00.
Meanwhile, Great Western Railway (GWR) said the train line between Par and Newquay was still closed, external and disruption was expected until the end of the day.
Urging the government to act, George said: “I think this is the worst storm in living memory.”
Creagh said she had held a meeting with water bosses over the issues.
“I remain very concerned that people in several areas in the South East and South West are experiencing water supply issues following both cold weather and Storm Goretti,” she said.