Details demanded over use of UK base in Indian Ocean involved in rendition flights.
"Reprieve intend to support Mr Madni in his legal action to ensure that British territory may never again be used to hide government wrongdoing."
Until last year, Britain repeatedly denied that Diego Garcia in the Indian Ocean had been used for rendition, with Reprieve cataloguing 54 such statements from the government.
In January 2008, David Miliband, the UK foreign minister, admitted two cases of illegal rendition via Diego Garcia and apologised for misleading both parliament and Reprieve.
Miliband admitted rendition flights entered and left UK territory but said the government had been unaware of them at the time.
Reprieve believes Madni was on one of the two flights confirmed by the government.
Madni, who now lives in Pakistan, was arrested on 11 January 2002 in Jakarta, Indonesia, and believes his journey to Cairo took in a refuelling stop at the US facility in Diego Garcia.
Reprieve, which represents several detainees held at Guantanamo Bay, says Britain must have known about Madni's alleged rendition as a specific chain of command was needed to authorise "unorthodox" flights.
It said records relating to flights to Diego Garcia before 2008 had been destroyed in mysterious circumstances and its case was aimed at forcing the government to come clean.
Clare Algar, executive director of Reprieve, said: "For too long, Diego Garcia has been used as a safe haven for the US and UK to commit criminal acts.
"It is about time this territory was subjected to the scrutiny of UK and international law.
"Mr Madni's case is the first step towards restoring the rule of law to Diego Garcia."
Madni said he was tortured by electric shocks to his knees during his interrogation in Cairo and he could no longer walk as a result and his nervous system had also been damaged.
Reprieve confirmed it would also take legal action in the US as part of a suit dealing with the case of another Guantanamo detainee, Shafiq Rasul, to allege that Madni's rendition in January 2002 was a criminal act.
Andrew Tyrie, a British member of parliament who heads a committee looking into Britain's role in rendition, said he hoped Reprieve's case would expose the truth.
"The litigation announced today will contribute to the growing amount of information on rendition and British involvement in it," he said.
"But the drip-drip of revelations about UK involvement in renditions is hugely damaging."
Tyrie said it was time for a full and open inquiry.
"It is now the only way to give the public confidence that we have got to the bottom of all of this," he said.
The foreign ministry said in a statement on Tuesday: "We have made our disappointment about these flights clear with the United States and secured firm new assurances that on no other occasion since September 11, 2001 has a US intelligence flight with a detainee on board passed through UK territory."