The parents of Madeleine McCann said they were disappointed after Portugal’s highest court threw out their libel case against a former detective who implicated them in their daughter’s disappearance.

Goncalo Amaral was ordered to pay €500,000 (£429,000) in compensation to Kate and Gerry McCann in 2015 by a Lisbon court over claims he made in his book and documentary about Madeleine, who vanished on the Algarve in 2007.

The decision was overturned following an appeal last year but the McCanns took the case to Portugal’s supreme court, which has now found against them.

While the judges’ official ruling is yet to be published, lawyers for the McCanns have been informed of their decision.

“What we have been told by our lawyers is obviously extremely disappointing,” the couple said in a statement. “It is eight years since we brought the action and in that time the landscape has dramatically changed, namely there is now a joint Metropolitan police-Policia Judiciaria investigation which is what we’ve always wanted.

“The police in both countries continue to work on the basis that there is no evidence that Madeleine has come to physical harm. We will, of course, be discussing the implications of the supreme court ruling with our lawyers in due course.”

Madeleine was three when she went missing from her family’s holiday apartment in Praia da Luz on 3 May 2007 as her parents dined at a nearby tapas restaurant with friends.

Amaral, who led the initial investigation into Madeleine’s disappearance, released the book three days after the case was closed in 2008. He later took part in a documentary for Portuguese television in which he claimed that Madeleine was dead, there had been no abduction and the McCanns had hidden her body.