Madeleine McCann’s parents have lost an appeal against the author of a book who alleged they were involved in the toddler’s disappearance.

Portugal’s Supreme Court ruled Kate and Gerry McCann cannot sue the former Portuguese detective who published the book for libel.

In 2015, a Lisbon court ordered Goncalo Amaral to pay Kate and Gerry McCann €500,000 (£429,000) in compensation for the allegations made in his book, Maddie: The Truth of the Lie.

Search for Madeleine continues

The book was published in 2008, three days after Portuguese authorities formally closed their inquiry and cleared the McCanns of any wrongdoing.

Mr Amaral argued in his defence that the claims in his book stemmed from the police investigation.

He also noted Portuguese media had already reported the possibility the parents may have played a role in Madeleine’s disappearance.

More than £50,000 was raised in support for the detective, donated via a Go Fund Me page, after he was ordered to pay damages.

Former detective Goncalo Amaral poses with his book during its launch in Lisbon in 2008 (AP)

The McCanns had sought €1.2m (£1m).

However, an appeals court overturned the conviction last year before reaching Portugal's top court.

The Madeleine McCann case Show all 25 1 /25 The Madeleine McCann case The Madeleine McCann case Madeleine McCann One of the last photos of Madeleine before her disappearance EPA The Madeleine McCann case Madeleine McCann Madeleine McCann was three when she was abducted during a family holiday in 2007 The Madeleine McCann case Top worn by a man that detectives investigate with connection to disappearance of Madeleine McCann A computer generated image of the distinctive burgundy long sleeve top worn by a man that detectives investigating the disappearance of Madeleine McCann are looking for The Madeleine McCann case Apartment in Portugal from where Madeleine went missing An aerial view of the Ocean Club apartments and pool where Madeleine McCann went missing Jeff J Mitchell/Getty Images The Madeleine McCann case Kate McCann Kate McCann speaks to the press outside the court house in Lisbon on 12 September 2013 following the first audience of the McCann couple's libel proceedings against former inspector Goncalo Amaral for a book written about the case of their missing daughter The Madeleine McCann case Kate and Gerry McCann Kate McCann and Gerry McCann before the start of the 'Miles for Missing People' charity run in Regent's Park in London, 2011 The Madeleine McCann case Kate and Gerry McCann Kate and Gerry McCann make an appeal at a press conference in the holiday resort of Praia da Luz, Portugal 7 May 2007 The Madeleine McCann case Kate and Gerry McCann The McCann's give an interview with a Spanish television channel at their home in Rothley The Madeleine McCann case Kate and Gerry McCann Madeleine McCann was abducted in Portugal in May 2007 AP The Madeleine McCann case Kate and Gerry McCann Preliminary forensic analysis on samples recovered from the McCanns' hire car raised the possibility of a match with Madeleine's DNA profile, according to the leaked report Getty Images The Madeleine McCann case Kate and Gerry McCann Pope Benedict XVI blesses a photo of four-year-old abducted British girl Madeleine McCann, while meeting her parents Gerry and Kate McCann, after his weekly general audience at the Vatican, 2007 Reuters The Madeleine McCann case Kate and Gerry McCann Gerald McCann and Kate McCann speak to the press on 4 May 2007 at the Ocean club appartement hotel in Praia de Luz in Lagos after Madeline vanished while her parents were out to dinner The Madeleine McCann case Portuguese police search for Madeleine Dozens of Portuguese police aided by dogs search for missing three-year old British girl Madelaine McCann in front of the Ocean club appartment hotel in Praia de Luz in Lagos The Madeleine McCann case Kate and Gerry McCann Gerald McCann and Kate McCann walk holding their two other children outside the Ocean club apartment hotel in Praia de Luz in May 2007 The Madeleine McCann case Madeleine McCann Madeleine McCann pictured at the age of three, left, and as she might have looked aged nine PA/Teri Blythe The Madeleine McCann case Kate and Gerry McCann The parents of missing Madeleine McCann have described as "pure speculation" reports in the Portuguese press suggesting that a chief suspect in the disappearance of their daughter was killed in a tractor accident four years ago. PA The Madeleine McCann case Tribute for missing Madeleine in Rothley, Leicesteshire Three year old Cally prepares to add a yellow ribbon to a floral tribute for missing Madeleine McCann in Rothley in Leicesteshire, 2007 The Madeleine McCann case Support for the missing Madeleine Everton captain Lee Carsley (L) leads his team onto the field, followed Mikel Arteta (C) and Manuel Fernandes (R) wearing Tshirts bearing a message of support for the missing British toddler Madeleine McCann, prior to the English Premiership match between Chelsea and Everton, at Stamford Bridge in London, 2007 The Madeleine McCann case Madeleine McCann A poster appealing for information about Madeleine McCann at a Spanish railway station PA The Madeleine McCann case BBC's Crimewatch reconstruction of Madeleine McCann's disappearance Former porn star Mark Sloan (L) was cast in the BBC's Crimewatch reconstruction of Madeleine McCann's disappearance BBC The Madeleine McCann case Clarence Mitchell holds two artist's impression of the new suspect McCann family spokesman Clarence Mitchell holds two artist's impression of the new suspect on 20 January 2008 in London. The description has come from British woman Gail Cooper, who was staying with her family close to the McCann's apartment in Portugal The Madeleine McCann case Image of a woman sought in the case Clarence Mitchell, the press spokesman for the McCann family, releases a photofit image of a woman sought in the search for missing Madeleine McCann Getty Images The Madeleine McCann case Suspect in disappearance of Madeleine McCann Police released two e-fits of suspect in disappearance of Madeleine McCann Getty Images The Madeleine McCann case Raymond Hewlett Convicted paedophile Raymond Hewlett, who is being sought in connection with the disappearance of Madeleine McCann PA The Madeleine McCann case A picture of a suspect An artist's impression of a suspicious man seen by a witness apparently watching the McCann family's apartment in Praia da Luz, Portugal, the day before Madeleine McCann went missing Channel 4

Madeleine disappeared from a holiday home in Portugal's Algarve region in May 2007, days before her fourth birthday.