Efforts will be stepped up tomorrow to suppress evidence of British involvement in the unlawful treatment of a UK resident, Binyam Mohamed, who says he was tortured in Pakistan, Morocco, and Afghanistan before being secretly rendered to Guantánamo Bay.

The foreign secretary, David Miliband, is appealing against six high court judgments ruling that CIA information on Mohamed's treatment, and what MI5 and MI6 knew about it, must be disclosed.

In a case which lawyers on all sides agree is unprecedented, counsel for the Guardian and other media organisations, Mohamed and two civil rights groups, Liberty and Justice, will argue tomorrow that the public interest in disclosing the role played by British and US agencies in unlawful activities far outweighs any claim about potential threats to national security.

Miliband's lawyers will tell Britain's three most senior appeal court judges, led by the lord chief justice, Igor Judge, that if the CIA material is disclosed the US might cut off the supply of intelligence to the UK, thus harming national security.

Since losing in the high court, David Millband has instructed one of the country's most expensive advocates, Jonathan Sumption QC, to represent his position. Sumption, who recently withdrew his application to become a justice of the supreme court after reports of "hostility" from other judges, is reported to earn up to £3m a year and is described by experts as one of the bar's "most formidable" opponents".

Sources say the decision to instruct Sumption comes amid growing concern within the government at the high court rulings, which officials had confidently expected to be in their favour.

In their six judgments, Lord Justice Thomas and Justice Lloyd Jones repeatedly challenged Miliband's claims. It is the first case in which the high court has questioned head-on claims by a government that evidence must be withheld on grounds of national security.

At the heart of the dispute is a seven-paragraph CIA document that the British government insists must remain secret. The two high court judges, who have seen the document, insist it does not contain any sensitive intelligence material. "What is contained in those seven redacted paragraphs gives rise to an arguable case of torture or cruel, inhuman and degrading treatment".

The judges stated after hearing arguments put by Miliband's lawyers: "It was in our view difficult to conceive that a democratically elected and accountable government could possibly have any rational objection to placing into the public domain such a summary of what its own officials reported as to how a detainee was treated by them and which made no disclosure of sensitive intelligence matters."

They added: "Indeed we did not consider that a democracy governed by the rule of law would expect a court in another democracy to suppress a summary of the evidence contained in reports by its own officials, or officials of another state, where the evidence was relevant to allegations of torture and cruel, inhuman or degrading treatment, politically embarrassing though it might be".

The two high court judges continued: "The suppression of reports of wrongdoing by officials in circumstances which cannot in any way affect national security is inimical to the rule of law," they ruled.

"A vital public interest requires ... that a summary of the most important evidence relating to the involvement of the British security services in wrongdoing be placed in the public domain ... Championing the rule of law, not subordinating it, is the cornerstone of democracy," they added.

The CIA information includes an account given to British intelligence "whilst [Mohamed] was held in Pakistan ... prior to his interview by an officer of the security service", the judges revealed earlier this year. The officer, known only as Witness B, is being investigated by the Metropolitan police for "possible criminal wrongdoing".

Miliband's claim that Britain's intelligence relationship would be jeopardised "lacks credibility on its face", the judges added.

The Guardian and other newspaper and broadcasting media groups argue that there is no wider public interest to be taken into account in the case than "open justice, the rule of law and democratic accountability".

Miliband was accused in the high court of wanting to suppress information about CIA activities even though details had already been disclosed by the Obama administration. Evidence that Miliband still wanted kept secret related to the question why "it was impossible to believe that President Obama would take action against the United Kingdom", the judges said.

Lawyers acting for the foreign secretary point to a letter sent by the CIA to MI6 in April, saying that if British judges ordered the information at issue to be disclosed the US might reassess its intelligence-sharing relationship with the UK. "The evidence that disclosure would cause serious harm to national security is overwhelming," Miliband's lawyers claim.

They point to a law lords ruling last year that the Serious Fraud Office could not pursue corruption allegations over arms sales by BAE Systems, Britain's biggest weapons maker, to Saudi Arabia because the Saudi government had threatened to stop intelligence-sharing with Britain. The case, in which Sumption also represented the government, has been described by critics as weakening the UK's reputation for observing the rule of law.