A couple alleging the UK was involved in their unlawful “rendition” to Libya urged the Supreme Court to rule there would be a “serious curtailment of fundamental rights” if parts of their legal fight were heard in secret.

Lawyers for Libyan dissident Abdel Hakim Belhaj and his wife Fatima Boudchar have described the proceedings in London before a panel of five justices, led by the court’s president Lady Hale, as “landmark”.

The hearing on Thursday relates to a judicial review action brought by the couple to challenge a decision by 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.

In December, two judges at the High Court made a ruling following an application by the Foreign Secretary which paved the way for “closed material proceedings” to take place when the judicial review case is eventually aired.

Ben Jaffey QC,  for the couple,  told the justices that closed material proceedings (CMPs) “are a serious curtailment of the fundamental rights to open and natural justice”.

Mr Jaffey said the issue in the appeal was whether a judicial review of a decision not to prosecute was a “criminal cause or matter”  within the meaning of the Justice and Security Act 2013.

Lawyers representing the couple say the “controversial and draconian” powers under the Act to hold hearings behind closed doors were “granted by Parliament solely for use in non-criminal proceedings”.

The High Court held that the couple’s case was not a criminal cause or matter for the purposes of the Act.

Mr Jaffey, arguing that the High Court’s “flawed” decision should be overturned, submitted that the term “in a criminal cause or matter” in the Act “includes challenges by way of judicial review to a decision not to prosecute”.

Mr Belhaj and his then-pregnant wife say they were unlawfully “rendered” from Thailand to Libya in March 2004.

Their lawyers say the couple allege they were “seized in a joint MI6-CIA-Libyan operation, tortured at a US prison in Bangkok, and ‘rendered’ to Gaddafi’s Libya”.

Law firm Leigh Day, representing the couple, said in a statement before the hearing that if the Government succeeds in having some hearings in secret, “Mr Belhaj and Mrs Boudchar, their lawyers, journalists, and the public, will be prevented from attending these sessions”.

Cori Crider, lawyer for the couple at human rights organisation Reprieve, said “criminal matters were explicitly excluded from the Justice and Security Act, and rightly so”.

She added: “With something this serious we, the British public, have a right to demand justice is done.”

The justices reserved their decision to a date to be fixed.