Their prime suspect for attacks on five other UK girls on the Algarve is an African burglar called Euclides Monteiro, who died in 2009.
The heroin addict used to work as a waiter at the Ocean Club resort in Praia da Luz on the Algarve but was sacked a year before Madeleine stayed there with her parents. He was killed in a tractor accident, aged 40, two years after the three-year-old vanished.
British detectives this week began a Europe-wide hunt for the paedophile, who was known to sneak into holiday homes late at night and molest girls aged between six and 12.
Nine attacks were reported to Portuguese police between 2004 and 2009.
Then three new victims came forward after Scotland Yard officers revealed on Crimewatch last year they were probing the possibility Madeleine had been snatched by burglars.
The incidents all took place in a 60km strip of the Algarve between Vale da Parra and Carvoeiro.
Detective Chief Inspector Andy Redwood, who is heading the inquiry, claimed the fiend could also have targeted Madeleine.
He said there was a possibility “she did not leave the apartment alive”.But last night Portuguese police accused the Met of “hijacking” their work.
A source said: “All the cases mentioned were investigated by us here. Monteiro was arrested but freed because of lack of evidence.’’
The Cape Verde immigrant had been working at a water treatment plant in the town of Lagos, near Praia da Luz, when the McCanns arrived for their holiday in 2007.
But days before Madeleine disappeared, he was signed off sick and did not return to work for two months. Mobile phone data analysis placed him near the McCanns’ apartment when she vanished.
A local source said: ‘“He is the main suspect for the incidents involving the girls on holiday and was questioned but there was insufficient evidence.”
Euclides’ widow Luisa, 40, has insisted her late husband and father of her child had nothing to do with Madeleine’s disappearance.
She said: “He may have broken into houses when he was younger because he was poor and had a drug habit. I know Euclides is an innocent man.”
British police were last night sifting through information contained in more than 250 calls and emails from the public following their television appeal to trace the sex attacker.
Asked last night about the Portuguese police’s claims about Monteiro, a Scotland Yard spokesman said: “We are not prepared to discuss it.”