Theory 1

One of the parents is responsible for Madeleine’s disappearance

The Portuguese media have suggested that Madeleine died in her holiday flat and that the child’s family and friends may have information about her death. “Gerry and Kate understand they need to be eliminated as suspects,” Mr Williams-Thomas said. “They were the last people to see Madeleine alive. Ninety per cent of murders are committed by someone who is known to the victim.”

Reports have suggested that the McCanns put their daughter to bed at 6pm. At 7pm, they went for a meal. At 9pm, Mr McCann is said to have checked on the sleeping girl and at 10pm Mrs McCann discovered that she was missing. This left Madeleine in the sole care of the McCanns, both doctors, for four hours and makes her father the last person to see her.

Most murdered children are killed by a relative or someone they know. “Children at that age can be very demanding and difficult,” Mr Williams-Thomas said. But the instinctive response of a parent to their child being hurt or injured is to seek medical help.

Theory 2

A friend is responsible for her disappearance

The three couples who were on holiday with the McCanns, some of whom shared the job of checking on the sleeping children by listening outside their rooms, will also interest police.

“They have knowledge that Madeleine was going to be in her apartment on her own. They had the opportunity to go into the apartment. They could go and see Madeleine without causing any disturbance.” But the failure to find the slightest trace of the child three months after she vanished in Praia da Luz weighs heavily against the McCanns, or any of the couples on holiday with them, being involved, the ex-policeman believes.

Had she died in the presence of any of those caring for her, it would have been by an unexpected accident rather than something planned. A panicking Briton would find it hard to hide the body of a child so quickly and effectively in a strange country.

Theory 3

She was abducted by a stranger

If the girl was taken by someone she did not know, it seems likely it was a child molester. Such predators would be most likely to snatch the child if they found her wandering outside.

“I don’t believe a paedophile was watching the apartment because most are completely opportunistic,” Mr Williams-Thomas said. “Since 1970, approximately six children have been murdered every year by paedophiles.” None of them had been stalked.

A paedophile would have to take a serious risk to wander into a holiday flat on the off-chance of finding a child alone. “I believe she was taken external to the apartment. This may have occurred by her wandering off. What’s key for me to know is if she had shoes on and if Gerry and Kate told her where they were. If they told her they were at the tapas bar, she may have wandered off to find them.”

Other scenarios involving strangers would have been detected by now. There were suggestions that Madeleine might have been taken by a kindly but deluded adult trying to replace a missing child. But such a surrogate parent would be unable to hide or persuade an unruly three-year-old to start calling them mummy or daddy in public. Fears that she was taken by a thief for sale can be disregarded. She is the wrong age and sex.

Theory 4

Madeleine wandered off and had an accident

“The sea is a fair walk away,” Mr Williams-Thomas said. “There isn’t anywhere obvious she could have come into some kind of danger. That place was swarming with people looking for her. I do not believe that she wandered off and had an accident.”

Mark Williams-Thomas is a child-protection expert

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