Experts are still trying to herd a pod of pilot whales back out to deeper water.
It is thought that up to 40 whales make up the group spotted off the Essex coast between Jaywick and Brightlingsea.
The mammals have been sheltering in an area with a number of mud and sand flats.
They were first seen off Essex on Tuesday but had been spotted elsewhere off the east coast as far back as the beginning of last week.
Marine experts are worried the whales could become trapped when the tide goes out.
People living nearby have been urged to keep their distance so they do not frighten the animals.
Police and a number of other boats are trying to herd the whales out of the shallow estuary and back into deeper waters.
Marine biologist Dr Helen Scales told Sky News that the reason the pod is in shallow waters and having difficulties is not known.
“We really don’t know why this happens,” she said, adding that something has probably confused the animals to send them off their usual course.
Dr Scales explained that pilot whales are so called because their pods are normally led by one individual. “They tend to stick together,” she said.
There is a chance that one of the whales is sick and others are staying with it, she added.
Speaking about the operation to direct the mammals back out into the North Sea, Dr Scales said: “The idea is not to be too aggressive, not to scare them off.”