Reprieve says hundreds of men are being held at the air base
A legal charity is to sue the UK government to force it to reveal the identities of two men being held in secret at a US base in Afghanistan.
Reprieve said the men were arrested by British troops in Iraq in 2004, handed to the US and "illegally rendered" to Bagram Air Force Base.
It says the men are among hundreds held "beyond the rule of law".
The Ministry of Defence said it had no reason to believe the allegations about their welfare were accurate.
It had previously told Reprieve, which is seeking to represent the men, that it would violate their rights under the Data Protection Act to reveal the identities.
The charity says that since 2004 the men have been held beyond the rule of law, far from their families, and have never been charged with an offence.
It says a review of their status by the US military was characterised by a US federal judge as falling "well short of what the Supreme Court found inadequate at Guantanamo".
Reprieve's director Clive Stafford Smith said: "These two men have been held in appalling conditions for five years, and for all that time the British government chose to do nothing.
"While we have not been able to identify their full names, we have learned that at least one of the men is now suffering from very serious mental problems as a result of his mistreatment.
"We have an urgent moral, as well as legal, duty to repair the damage his rendition has caused."
Mr Stafford Smith added: "How many more times is the government going to say one thing - that they never cover up complicity in torture - while doing the opposite?
"Here, the government admits its involvement in the crime of rendition, says it apologises, but then does nothing to reunite the victims with their legal rights."
Reprieve said it has tried to identify the men through independent investigation, but the task has been severely hampered by "a shroud of secrecy" around Bagram.
A spokeswoman for the charity told the BBC: "There's so much secrecy surrounding this prison. It's like Guantanamo, but far, far worse."
However, the charity said interviews with prisoners who have been released from the prison, had tentatively identified the two men as Salah el Din and Saifullah, both from Pakistan.
Salah el Din, in particular, suffers from serious mental problems as a result of his mistreatment in custody, Reprieve said.
Originally built by the Soviet military during its invasion of Afghanistan in the 1980s, Bagram is now the main base for the US-led coalition force.
The base near Kabul can hold up to 10,000 troops. It is under US command and control but forces from other coalition nations also use the facility.
It also houses the main prison facility for people detained by US forces across the country, and can hold up to 1,000 prisoners.
The MoD said it was considering the legal points Reprieve had made in a letter and would respond in due course.
A spokesman said: "These individuals are in the custody of the US government.
"We have no reason to believe that Reprieve's unsubstantiated allegations about their welfare are accurate.
"The US has assured us the detainees are held in a humane, safe and secure environment within the detention facility, which meets international standards for the care and custody of detained persons.
"The International Committee of the Red Cross has had access to these detainees."