Three UK men held at Guantanamo Bay have been "severely tortured", their lawyer has said.
Omar Deghayes has been held for three years.
Lawyer Timothy Otty told the High Court there was "compelling evidence" of abuse - a claim denied by the US.
The men have asked the court to force Foreign Secretary Jack Straw to press for their release.
Mr Straw will make representations for Bisher al-Rawi, an Iraqi citizen with UK residency. But the government says it cannot act for two other men.
It says Jamil el-Banna and Omar Deghayes are not UK citizens but it has conveyed concerns about the three men to the US on a purely humanitarian basis.
They are among at least five UK residents still thought to be held at the US-run camp in Cuba.
Mr Otty, addressing two judges at the start of a three-day hearing, said further ill treatment was a "real risk" for the men, while their families were suffering from "intense distress".
He said that in the case of Mr al-Rawi "it has now been conceded that the foreign secretary will be making representations".
In documents submitted to the court, Mr el-Banna and Mr al-Rawi were alleged to have connections with al-Qaeda through radical Muslim cleric Abu Qatada.
Mr al-Rawi has always maintained that he had contact with Qatada which was "expressly approved and encouraged by British intelligence".
He said intelligence staff had told him they would help him if he ever ran into trouble.
Mr Otty said documents annexed to a statement made by a security service official, referred to as "witness A", established there had been "communications" between British and US security services relating to the Mr el-Banna and Mr al-Rawi before their arrests.
Mr Otty said: "We will certainly be contending there has been real injustice, and there is a causal link on the part of those acting for the UK in that injustice."
Businessman Mr al-Rawi, who is in his late 30s, was reportedly sent to England in 1985 after his father was arrested by Saddam Hussein's secret police.
Amnesty says he and his friend Mr al-Banna, a Jordanian refugee who had been living in north-west London, were arrested in November 2002 at Banjul airport, during a business trip to Gambia, on suspicion of having links to terrorism.
Libyan-born Mr Deghayes, 36, of Brighton, has been held at Guantanamo for three years and was on a hunger strike, Mr Otty said.
He was arrested in Pakistan and accused of committing terrorist acts against the United States, but his lawyers claim it is a case of mistaken identity.
He fled Libya for Britain in the 1980s after his father was assassinated. He was granted refugee status in the UK, where he was educated and applied for British citizenship.
Christopher Greenwood QC, appearing for the foreign secretary, told the judges that the government was "attaching considerable weight" to the US denial that torture or inhuman treatment had taken place at Guantanamo Bay.
The government would "certainly not accept that there was compelling evidence that the men have been tortured".
Mr Otty highlighted reports critical of Guantanamo Bay, including one by MPs and the United Nations.
Mr Otty told the judges: "The situation at Guantanamo Bay has been roundly condemned even before the allegations of torture and the wealth of material supporting those allegations entered the public domain."
The latest Foreign Office statement, issued last week, said that given the "ongoing sensitive nature of the discussions in relation to Guantanamo Bay as a whole" it would be both "ineffective and counter-productive to make individual requests".