UK police say they know who kidnapped British four-year-old Maddie McCann in Portugal seven years ago, and are angry and frustrated they cannot swoop in and arrest the men.

Three men who were members of a gang of thieves are now prime suspects in Maddie's abduction from a Portuguese beach resort in 2007.

Scotland Yard police officers have identified the men in the enduring mystery of the girl's disappearance.

British detectives have analysed mobile phone records of the men who are believed to be members of a burglary gang preying on tourists in the Algarve beach resort town of Praia da Luz around the time Madeleine vanished.

The police have tracked a high volume of calls between the three men in the hours after Madeleine was reported missing from the holiday apartment rented by her parents, Kate and Gerry McCann.

News_Image_File: Kate and Gerry McCann outside the hotel in Portugal where their 4-year-old daughter Maddie was abducted in 2007. Picture: AFP.

They are frustrated with the incompetence of the Portuguese investigation into the case, and with delays in pouncing on the suspects.

The UK police's leading scenario is the thieves broke into the apartment, disturbed the young girl and fled with her in what was a burglary gone wrong, rather than earlier speculation she was targeted by paedophiles or child abductors.

Mr and Mrs McCann, who had been dining with friends at a nearby location returned home to find their daughter had vanished.

Checks into the three men's criminal history and family backgrounds are believed to be made, but UK authorities are hamstrung by the fact they cannot make arrests in a foreign country, and none of the men are British.

News_Image_File: Photograph of missing Madeleine McCann taken during the holiday at Praia Da Luz, Portugal, from where she was kidnapped in 2007. Picture: AP.

Widespread criticism of the bungled Portuguese police investigation into the McCann case includes they gave little weight to the fact the McCann's holiday flat ad been broken into.

Scotland Yard believes the thieves accidentally woke Madeleine up, panicked and decided to take her with them when they fled the premises.

The burglars are now the focus of their inquiries, which has been thwarted by Portuguese authorities refusal to co-operate formally in a joint investigation.

UK detectives are said to be keen to arrest the men for questioning, but have to await diplomatic negotiations between the respective governments for permission to operate within Portugal.

News_Image_File: UK police believe they know who kidnapped Madeline McCann, the 4-year-old daughter of Kate and Gerry McCann (above) in 2007. Picture: AFP.

They have also discounted a theory favoured by Portuguese police, that a 40-year-old former employee at the holiday complex where the McCanns stayed was Madeleine's kidnapper.

The man has since died in an accident.

The British detectives who have examined the records of mobile of thousands of people who were in Praia da Luz in May 2007 describe the phone analysis as "compelling".

In another development, Kate and Gerry McCann have been refused permission to give evidence at a defamation trial in Portugal over a book written by a former local police chief about the case.

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