The two men are thought to be in detention at Bagram Air Base
A legal rights charity has accused the government of misleading Parliament over two men arrested by the British military in Iraq.
Reprieve says British forces handed the men to the US military who then took them to Afghanistan in 2004.
It says one of them is a Shia rice trader and not part of a banned group linked to al-Qaeda, as ministers claim.
The Ministry of Defence said the prisoners' "initial detention" had been appropriate and legitimate.
In February, the then Defence Secretary John Hutton confirmed to Parliament that British forces had been indirectly involved in two cases where the US had moved prisoners from one country to another.
The procedure of moving detainees for questioning in a country where torture is not illegal, dubbed extraordinary rendition, has been internationally criticised by human rights campaigners.
The individuals detained in this operation were members of Lashkar-e-Taiba and were a significant threat to the lives of Iraqi civilians and to coalition forces
Ministry of Defence
For years, the government denied Britain had been involved in rendition.
However, Mr Hutton told Parliament that in February 2004 British forces handed over two individuals to US forces in line with normal operational guidelines. The US then moved the men to Afghanistan, where they remain.
"The individuals transferred to Afghanistan are members of Lashkar-e-Taiba (LeT), a proscribed organisation with links to al-Qaeda," Mr Hutton said.
"The US government have explained to us that those individuals were moved to Afghanistan because of a lack of relevant linguists to interrogate them effectively in Iraq.
"The US has categorised them as unlawful enemy combatants and continues to review their status on a regular basis.
"We have been assured that the detainees are held in a humane, safe and secure environment that meets international standards that are consistent with cultural and religious norms."
Human rights groups claimed this amounted to colluding in rendition.
On Monday, Reprieve said that it had since established that one of the two men, Amanatullah Ali, is a Pakistani rice trader who belongs to the Shia branch of Islam.
It questioned whether Mr Ali could be a member of LeT because it draws its support from Sunni Muslims, rather than Shias.
Amanatullah Ali is believed to be one of the two detainees
Clive Stafford Smith of the charity said that they had not been able to confirm the identity of the second man, but he is thought to be called Salahuddin and was now suffering from "catastrophic" mental health problems.
He said the claim that the men had to be moved to Afghanistan because there were no adequate translators in Iraq did not hold water as Salahuddin spoke Arabic - Iraq's primary language.
"Government ministers misled Parliament and the country by denying that we had anything to do with rendition and then, when John Hutton 'apologised' for this, he misled Parliament again.
"The government now appears unwilling to admit that they are still propagating falsehoods."
The charity was demanding access to both men, thought to be in detention at Bagram Air Base, in an effort to help their cases, Mr Stafford Smith added.
Our mindset has been not to challenge the American approach to dealing with prisoners and suspects
Former Conservative shadow home secretary David Davis said the government had an obligation to "get this man a proper trial or released back to his family".
"It's simply exercising our legal responsibilities as the people who caught him in the first place.
"I suspect we don't have detention facilities for people we pick up so we hand them off to the Americans - and it was an accident not to challenge it.
"But that has been our problem all along. Our mindset has been not to challenge the American approach to dealing with prisoners and suspects and that's when we end up with Abu Ghraib and Guantanamo and now Bagram."
David Davis: "I want the government to put right the wrong that they started"
Liberal Democrat foreign affairs spokesman Edward Davey called for Sir John Chilcot to investigate the incident as part of his inquiry into the Iraq War.
"The government appears to have misled Parliament over a number of facts that were central to its attempted defence of the rendition of these prisoners," he said.
"[Defence Secretary] Bob Ainsworth must come to the House of Commons and set the record straight."
An MoD spokeswoman said: "The operation referred to by John Hutton in his February statement was directly related to threats to security and stability in Iraq.
"The individuals detained in this operation were members of Lashkar-e-Taiba and were a significant threat to the lives of Iraqi civilians and to coalition forces."
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