A couple who recently received an apology from the UK Government over their rendition to the regime of dictator Muammar Gaddafi have won a Supreme Court ruling they say has upheld the “key principle of open justice”.

Lawyers for Libyan dissident Abdul Hakim Belhaj and his wife Fatima Boudchar urged five justices during a hearing in March to find there would be a “serious curtailment of fundamental rights” if parts of their civil legal battle, arising out of what happened to them in 2004, were heard in secret.

Their appeal at the UK’s highest court centred on a High Court ruling paving the way for “closed material proceedings” in a judicial review action they launched to challenge a decision of the Director of Public Prosecutions (DPP) not to prosecute former senior M16 officer Sir Mark Allen over his alleged role in the rendition.

The DPP concluded there was insufficient evidence against him.

Since the Supreme Court hearing, after which the judges said they would give their decision at a later date, it has been announced that Britain has reached a “full and final” settlement with the couple over the rendition.

Although the judicial review proceedings have been settled, a panel of justices, including the court’s president Lady Hale, said on Wednesday that a judgment was still being given “in view of the importance of the legal issue”.

The court allowed the couple’s appeal by a majority of three-to-two against the decision of two judges at the High Court in December following an application by the Foreign Secretary.

Mr Belhaj said in a statement: “I am delighted the Supreme Court has upheld the key principle of open justice today.

“I have achieved justice in my case. I hope this judgment will allow others to do the same.”

Rosa Curling, from the human rights team at law firm Leigh Day, who represented Mr Belhaj and Ms Boudchar, said: “Although our clients’ claim against the DPP is not proceeding, they are delighted the Supreme Court has upheld their belief in the UK justice system: One which is fair, open and transparent.

“To have allowed secret hearings in cases like theirs, which relate to criminal causes or matters, would have closed off open justice to many victims of crimes.

“The judgment today is an important safeguard against the Government’s attempt to extend secret hearings into yet further types of proceedings, and allow the Justice and Security Act to apply in areas not envisaged by Parliament.”

During the Supreme Court hearing it was argued that a judicial review of a decision not to prosecute was a “criminal cause or matter” within the meaning of the 2013 Act, and therefore secret hearings were not allowed.

The couple challenged the High Court’s “flawed” ruling that their case was not a criminal cause or matter for the purposes of the Act.

Attorney General Jeremy Wright told the House of Commons in May that the Prime Minister had written to Mr Belhaj and his wife to apologise for the “appalling treatment” they received.

The settlement included the withdrawal of claims against the British government,  former foreign secretary Jack Straw and Sir Mark. Mr Wright stressed there was no admission of liability from any of the defendants.

Theresa May wrote to the couple saying the UK Government’s actions “contributed to your detention, rendition and suffering”.

The couple have fought a long legal battle over their claim that they were kidnapped and returned to Libya in a joint MI6-CIA operation linked to Tony Blair’s infamous “deal in the desert” with Gaddafi.

They said that after three years evading Gaddafi’s agents after fleeing Libya, they were seized in Malaysia and sent to Thailand for rendition to the north Africa country as a result of a tip-off from UK intelligence.