Jodie Loughlin, six, and her brother Tom, four, were last seen by their parents running through crowds of families towards the waves on Sunday evening as the tide came in. They disappeared from their parents' sight within minutes.
As dusk fell last night, police continued to comb the four-mile area of coast near Hunstanton, joined by a firemen, coastguards, mountain rescue experts and volunteers. But they found no sign of the children, who cannot swim, and fears grew that they had been swept out to sea.
Their parents, Kevin Loughlin and Lynette Thornton, both 37, from south London, were fighting to come to terms with what had happened.
Superintendent John Hale, who is co-ordinating the search, said there was no indication that the children had been abducted. The search was to be resumed atsunrise today.
"The children's parents have been absolutely amazing," Supt Hale said. "Everything must have gone through their minds, I am sure. But they have nothing to reproach themselves for. Children get separated from their parents on beaches all the time. We know that it only takes a minute."
The family had arrived for a week's holiday in Norfolk on Saturday. Mr Loughlin, a computer consultant, was the last known person to have seen the children and was among searchers who scoured beaches, dunes and woodland for six hours on Sunday night.
One woman holidaymaker, from Cambridgeshire, reported seeing two children who fitted the description of Jodie and Tom playing alone in the surf at around 6.30pm on Sunday, about a mile from where they were last seen. Police are also examining a private video of the scene on the beach on Sunday.
The beach at Holme was particularly busy at the weekend because Hunstanton was celebrating its 150th anniversary. Thousands of families visited the resort, which is famous for its golf course, sandy beaches, coastal resorts and nature reserves.
But Holme is also notorious for its unpredictable waters and uneven sands which has led to swimmers being caught out by the incoming tide.
The incident is the second tragedy involving holidaymakers there in the past two years. An eight-year-old boy from Leicester was buried alive in a sand dune in the resort.
The body of a missing eight-year-old boy was found on a beach near Skegness, Lincolnshire, yesterday after a three-hour search by 100 volunteers joined police, coastguards and lifeboat crews in a search. A police spokesman said there were no suspicious circumstances.Reuse content