Last night police sealed off the area surrounding the picturesque beach, which minutes earlier had been busy with tourists and locals enjoying the sunny Easter school break.

Officers set up a major crime investigation unit as forensic experts began combing the scene of the grisly find.

Mr Carswell, who was working in an apartment on the beachfront, just metres from where the head was found, added: "There were two red-headed little girls, one aged about six, and the other four or five, and they were playing at the water’s edge. 

"I saw them poking about a black bin bag, when they suddenly took off screaming in a hurry, which I thought was a bit strange.

"I saw them come back with their mother, and I asked her what was going on.

"She said she thought the girls had found a head, and that she had called the police.

"They went to the black bin bag, and when they opened it up, I saw some hair, and it was plainly a head."

Detective chief inspector Graham McMillan of Tayside Police, who is leading more than 40 officers in the massive investigation.

He confirmed that the head and hand belonged to an unidentified woman.

The murder victim’s remains showed she had long brown hair, but it is not known what age or age or race she was.

DCI McMillan said: "We will soon be removing the body parts, and conducting a more detailed examination of them.

"It is still too early to say how long it has been in the water.

"We have conducting only very tentative examinations at the moment.  We need to get it into a controlled environment where it will be subject to very detailed and painstaking investigations.

"The children who made the discovery are very upset, and are being cared for by their parents."

Louise Tiffney went missing in 2002 aged 43, three days before her son Sean Flynn had been due to appear in court for killing his best friend and cousin in a high speed car crash.

Flynn’s cousin Paul Ross, 18, and best friend Christopher Magee, 18, died when he crashed at speed in Mid-Calder, West Lothian, while chasing another car in their BMW.

Two years ago Mrs Tiffney's mother, Mary , 74, said she was convinced her daughter's remains were dumped and washed out to sea off the East Lothian coast.

DCI McMillan continued:  "We had very heavy rain on Monday night, and the head was found at the high water mark.
"We are trying to preserve the scene as much as possible, and we will probably conduct a further search tomorrow.

Local councillor David Fairweather fears the incident could be a by-product of problems emerging in the town.

He said: "I feel most sorry for the two little girls. It’s horrific that they should be subjected to something like this."

Housewife Linda Sloane, 40, added: "My kids play on that beach all the time. I don’t know how I’d cope if they found something like this."

Dr Adrian Linacre senior lecturer in forensic science Strathclyde University, said: "The remains are described as a recognisable as a woman’s, so they clearly not been in the sea for very long.

"Its hard to say, because for example, they may have been kept in a freezer for years before.

"Pathologists will first of all try to match up the body parts. They have an advantage in that they will potentially have dental records, DNA, fingerprints and maybe even a recognisable face.

"It will depend on whether this person’s details are on any of these databases, and whether they can be matched up to any missing persons.

"The manner in which the remains were dismembered, and the weapon used to do it will also give clues."