Goncalo Amaral's book Maddie: The Truth Of The Lie claims she died in the family's holiday apartment in the Algarve and her parents covered up her death by faking her abduction.

Mr and Mrs McCann strongly deny the claims, and are pursuing a defamation case against the former detective, who led the initial investigation into the Madeleine case.

In February, a Portuguese judge upheld an injunction banning any further sale or publication of his book and DVD documentary.

But now a Portuguese court has overturned the ruling, saying the ban had broken "a constitutional and universal right: that of opinion and freedom of expression."

"The contents of the book do not breach the basic rights of the plaintiffs," the court said, according to the Jornal de Noticías newspaper.

Mr Amaral was delighted by the decision, telling Portugal's Lusa news agency: "The book is an exercise in freedom of speech.

"Portuguese democracy has won, as banning the book was unconstitutional."

A spokesman for the McCanns was unavailable for comment

Their lawyer Isabel Duarte said: "We must return about 8,000 copies of the books to the editor, which will probably go on sale."

When the initial injunction was upheld, the McCanns vowed to continue looking for their daughter and appealed once again for help from the public.

They said Mr Amaral's "painful and personally damaging" allegations had caused "significant, ongoing damage" to the hunt for Madeleine.

Mr and Mrs McCann believe their daughter, who was three when she vanished in Praia da Luz on May 3 2007, was snatched and is still alive.

She disappeared while the couple dined with friends at a tapas bar some 90 yards from the apartment.