Severn Trent issued a warning in Derbyshire and Leicestershire on Friday after it found high levels of the chemical at a reservoir.
About 3,700 properties are affected in postcode areas DE11, DE15, DE65, DE73 and LE65.
It is hoped the water will be safe to use later, although the firm said customers can now flush their toilets.
Latest updates: Severn Trent Water problems
Severn Trent has been handing out free bottles of water to affected customers at Sainsbury's in Swadlincote, Derbyshire, and Tesco in Ashby-de-la-Zouch, Leicestershire.
Nigel Thornylowe, who lives in Woodville with his two children, said it was a "nightmare".
"We got caught up in the frenzy yesterday and unfortunately... we haven't got any bottled water," he said.
"We've tried in vain but all the supermarkets have run out."
He said the situation had been poorly managed and bottles of water should be distributed at more locations than just the two supermarkets.
But other residents have been looking out for their neighbours with one couple filling up the water carrier in their caravan and distributing it to elderly neighbours.
And another woman said she coped on Friday night by "drinking spritzers" instead of water.
In a statement, the firm tried to reassure customers who may have drunk the water that, if they did not notice a strong chlorine smell or taste, then it was "unlikely to have caused any harm".
But it added that anyone with concerns should speak to a doctor.
"We're very sorry for the inconvenience this has caused but we want to reassure customers that this is a precautionary measure due to the levels of chlorine in the water supply," it said.
Thousands of people are still being told they should not use their water because of high levels of chlorine.