The description is the first confirmed sighting of the children anywhere near the beach at Holme, near Hunstanton, since the search began 11 days ago.
Police said that a middle-aged woman had come forward saying she had heard the children's mother Lynette Thornton, 37, call out to four-year- old Tom, who was lagging behind as the family walked across the beach.
Police Sergeant Peter Thompson said that the witness's description was a "very healthy development with very little discrepancy from a perfect match".
He added: "This was as near to 100 per cent a description as one could get, with so many detailed points."
Yet despite the woman's report, police say they are nowhere nearer to tracing the movements of the two children after they left their parents and ran towards the sea.
Yesterday the police renewed their appeal for two women to come forward. They were walking across a golf course near the beach and had remarked on two shrimp nets that Jodi, six, was carrying.
The police also said they wanted to speak to a man who kicked a black and white beach-ball to the family, and a middle-aged couple who were seen talking to two children in a boat.
The search has been complicated over the past 11 days as Kevin Loughlin, 37, and his wife, from Norwood, south London, became increasingly confused about the circumstances surrounding the case. For six days, police understood that the family had been near golf links at the village of Holme next the Sea when the children ran off.
It was not until Friday of last week that Mr Loughlin was calm enough to pinpoint that they had been at Gore Point, a narrow split a mile nearer The Wash. However, on Tuesday of this week, a third location between the golf links and Gore Point was given as the spot.
Yesterday, police were granted use of a large computer system, the Home Office Large Major Inquiry System (Holmes), to deal with more than 700 calls which had been logged since the beginning of the search.
Holmes allows detectives to sift swiftly through large amounts of information gathered on a major inquiry, and to spot links and patterns in evidence.Reuse content