Dublin-born Mr Halligen unsuccessfully worked on the case for about six months in 2008 but fell out with the couple because he delivered so little.
It is estimated that his fees swindled the Madeleine Fund out of £300,000. A source said: “I believe the police are looking into the possibility he fell over and cut his head badly.
He was known to be a heavy drinker.” The scene where he was found was said to be heavily blood-stained. Mr Halligen was found last Monday at the Surrey home of his girlfriend.
A police spokesman said: “We were called to an address in Guildford on Monday after a report of a man in his 50s having been taken unwell, who subsequently died.
The death is being treated as unexplained and a fi le will be passed to the coroner.”
A former colleague, defence consultant Tim Craig-Harvey, wrote online: ‘‘The lies and alcohol finally caught up with him.”
While desperate for a breakthrough in the hunt for their daughter, doctors Kate and Gerry, of Rothley, Leicestershire, hired Halligen, agreeing a £500,000 fee with Oakley International.
His boasts of employing former CIA and FBI detectives encouraged the couple to believe he could finally get some strong leads.
However, within a few months of hiring him the couple began having serious doubts about his claims. Images from satellites turned out to have come from Google Earth.
Rumours circulated that while on the investigation Halligen was staying at top hotels and eating well at expensive restaurants, while the scope and depth of the investigation was beyond his ability.
After being sacked by the McCanns, he was arrested in Britain and extradited to America for fraud on an unrelated case. He pleaded guilty to defrauding Trafigura, based in the Netherlands, who had hired him to help free two company executives arrested in Ivory Coast in 2006.
He received about $12million to provide “security, intelligence and public relations”. The Washington Post reported: “Owners of Washington restaurants remember him spending thousands on long, boozy days and evenings. He travelled everywhere in a chauffeured Lincoln.”
One restaurant owner said he and his staff called Halligen James Bond because of his stories of spy derring-do and his habit of flashing large sums of cash.
After 42 months behind bars in the US, he was deported to Dublin.
Four years ago he was interviewed for a Channel 5 documentary and denied misusing any of the Madeleine Fund money, saying: “It is gross distortion of what was actually happening.”
A source close to Kate and Gerry McCann said they had terminated their contract with Oakley International at the end of 2008 and had not had anything to do with Kevin Halligen since.