Mr Mohamed, a British resident, claims he was tortured
Lawyers acting for a UK resident being held at Guantanamo Bay are launching a new High Court bid to have alleged evidence of torture made public.
Binyam Mohamed, 30, says he was tortured before being flown to the US detention camp in Cuba.
Last week, judges refused to order the disclosure of a summary of US reports on his detention, citing a threat to US intelligence-sharing with Britain.
The US denies that evidence against Mr Mohamed was obtained through torture.
Ethiopian national Mr Mohamed is the last recognised British resident to be held at Guantanamo Bay.
He had lived in the UK since the age of 15, but was arrested in Pakistan in 2002.
He claims he was secretly flown to Morocco and tortured before being moved to Afghanistan and finally, in 2004, to the US naval base in Cuba, where he remains, although charges against him were dropped last year.
Earlier, Lord Justice Thomas and Mr Justice Lloyd Jones had ruled that some parts of papers referring to Mr Mohamed should remain secret, following the threat from the US to halt the sharing of information on terrorism.
In making the decision the judges criticised that threat, saying it was "difficult to conceive" that a democratically-elected and accountable government could rationally object to the summary of Mr Mohamed's treatment by US agencies being published.
However, they said Foreign Secretary David Miliband believed there was a "real risk" that the potential loss of intelligence co-operation would seriously increase the threat from terror faced by the UK.
Mr Miliband later insisted there had been "no threat" from the US.
He added that confidentiality was key to intelligence sharing, a view backed by the White House.
Mr Mohamed's solicitors, Leigh Day and Co, and human rights campaign group Reprieve are now attempting to persuade the judges to reconsider their decision.
They argue that the court relied on misleading evidence provided by the UK government.
"In court, disclosure was resisted because of US threats to downgrade the security relationship if it was disclosed," said Richard Stein, partner at Leigh Day and Co.
"Now it is said, by the Foreign Secretary, to be because of a mutual understanding about how intelligence material is treated.
"In light of the weight given by the court to the 'threat', that is a substantial difference.
"When information is passed to any democracy governed by the rule of law it will be recognised that its courts might, in certain circumstances, order its disclosure.
"One of those circumstances would be where, as in this case, it discloses evidence of torture."
The US denies that evidence used against Mr Mohamed was obtained through torture.
Today's preliminary hearing is expected to be brief, providing directions and a timetable for a full hearing in the near future.
On Monday, US military lawyer Lt Col Yvonne Bradley flew to Britain to urge the Foreign Office to press harder for Mr Mohamed's release.