Calls to Severn Trent Water's service centre have increased by 220% since Sunday, with the majority being about frozen pipes.
The water firm said people ringing its call centre had faced delays of up to 90 minutes as callers jammed the lines.
It said people should not contact them if their pipes froze but instead wait for them to thaw naturally.
The service centre dealt with 2,500 calls alone between midnight and 0930 GMT on Tuesday.
The firm said it normally dealt with 1,700 calls throughout an entire day during non-wintry conditions.
Senior operations manager Fraser Pithie said: "Unfortunately we're not able to do anything to help you restore your water supply.
"We do need to be able to deal with calls about our water mains and sewerage networks, so we can respond and restore service where it may have failed.
"If your neighbours' supplies are unaffected, it is most likely that your internal water pipes are frozen."