Two terror suspects, including British citizen of Indian origin Haroon Rashid Aswat, on Thursday lost their High court battle to avoid extradition to the United States.
Aswat, 31, faces trial on charges of plotting to set up a US camp to train fighters for Afghanistan.
Babar Ahmad, the other suspect, who is of Pakistani origin, is accused of running websites inciting murder, urging holy war and raising money for the Taliban.
Lawyers for the men had claimed that despite US assurances, there was 'a real risk of fundamental injustice'.
But Lord Justice Laws, sitting in London with Justice Walker, said the men's legal team had not proved to a required standard their allegations that the US might violate undertakings given to the UK that the men would be fairly treated.
Edward Fitzgerald, QC, representing both men, had earlier asked the judges to stop the extradition process.
He has said there was a danger their human rights would be abused, despite the assurances from US authorities.
Fitzgerald said the two were in danger of being kept indefinitely at Guantanamo Bay, taken to a third country for questioning or tried and sentenced by a military tribunal as enemy combatants.
However, lawyers for the US authorities had said the assertions made by Fitzgerald were 'speculative'.
They said the assurances they had been given, that the men would be fairly treated, were 'an intrinsic, accepted and flexible tool in the extradition process'.
