A husband and wife who were victims of a joint MI6-CIA “rendition” operation have been plunged into a Kafkaesque nightmare by the attempt to have their claim against the former foreign secretary Jack Straw heard in secret, the high court has been told.

Abdel Hakim Belhaj, a Libyan dissident, and his wife, Fatima Bouchar, who were abducted in 2004 and flown against their will to Tripoli, are suing Straw and the former MI6 counter-terrorism chief Sir Mark Allen – as well as MI6 and the Foreign Office (FCO) – for their alleged role in the operation.

Their claim is supported by a mass of documents discovered during the 2011 Libyan revolution, which detail the way in which Allen and MI6 took credit for the tip-off that enabled the CIA to kidnap the couple in Bangkok and fly them to one of Muammar Gaddafi’s prisons.

Government lawyers tried to persuade the supreme court to strike out the claim, but failed and are now asking the high court to agree to have much of the case heard in secret under the terms of the controversial Justice and Security Act.

The high court has heard that MI6 and the FCO have not given any indication – even during secret sessions – whether they intend to contest the allegations.

“Absent that, we are in a wholly Kafkesque situation in which I do not know the response of the defendants to the most basic points,” said Richard Hermer QC, for Belhaj and Bouchar.

The claim is based on documents that have been reported upon globally and never challenged, said Hermer, adding that the CIA’s post-9/11 rendition programme is so widely understood that a hearing in open court would not damage UK-US relations.

The “exceptionally serious allegations” were supported by a wealth of evidence, and hearing the case in secret raises “a very serious risk of dragging justice into disrepute”, he said.

Rory Phillips QC, for the government, Straw and Allen, said the open justice principle was important, “but parliament has recognised there is a higher public interest” in allowing the government to defend itself more fully under the provisions of the Justice and Security Act.

Straw denies the allegations against him and has said he welcomed the chance to defend himself.

However, Phillips said that if the high court did not agree that the government’s evidence was so sensitive that it should be presented only in secret, the government might still forbid Straw and Allen from relying upon it, meaning they would be in breach of the Official Secrets Act if they attempted to do so in open court.

The judge, Mr Justice Popplewell, described this scenario as having “rather troubling ramifications”.

Bouchar had been pregnant at the time of the abduction. She was released from prison shortly before giving birth. Her husband, who had been a leading member of an anti-Gaddafi militia, the Libyan Islamic Fighting Group (LIFG), was detained for six years.

He alleges he was severely tortured throughout this time. He also says he was interrogated by British intelligence officers, who indicated to him that they knew he was being tortured.

A second LIFG leader was also abducted and flown to Tripoli along with his wife and four children. His damages claim against the British government was settled when he was paid £2.2m. Belhaj says he will settle for £1, but insists he and his wife also receive an apology.

Separately to the damages claim, lawyers for Belhaj and Bouchar are seeking a judicial review of the decision to not bring criminal charges against Allen. The decision was announced last year by the Crown Prosecution Service (CPS) following a lengthy Scotland Yard investigation.

Hermer told the high court that the CPS announcement had confirmed that the British government had been involved in the couple’s rendition. He said it also confirmed that Allen was the suspect in the police investigation, and that he had sought political authority for some, but not all, of his actions. This authority must have been sought from Jack Straw, as foreign secretary, Hermer said.

Popplewell will make a decision on the government’s secrecy application later in the year.