The Prime Minister said he was “very pleased” the European Court of Human Rights in Strasbourg had rejected the men’s claims they could face prison conditions and jail terms in the US which would amount to “torture”.
Speaking during a trade mission to South East Asia, Mr Cameron said: “I am very pleased with the news.
“It is quite right that we have proper legal processes, although sometimes one can get frustrated with how long they take.”
Relatives of the five terror suspects however have vowed to fight the European ruling, accusing Britain of “subcontracting” justice to the United States.
Family members of Babar Ahmad, a 36-year-old computer expert and alleged terrorism fundraiser, called for a public inquiry.
Ahmad, has been held in a UK prison without trial for nearly eight years.
His father Ashfaq said: “British justice appears to have been subcontracted to the US – this should be immediately rectified by putting Babar on trial in the UK… and ordering a full public inquiry into the matter.”
Lawyer Fahad Ansari, who worked on the family’s campaign, said he believed there would be an appeal by the men in the coming months.
He added: “It’s an absolute travesty of justice.”
The five men had argued that in the US they could face prison conditions and jail terms which would expose them to “torture or inhuman or degrading treatment or punishment” in breach of the European human rights code.
Alongside Ahmad awaiting extradition is radical Muslim preacher Hamza, currently serving a seven-year sentence in Britain for soliciting to murder and inciting racial hatred
Three others – Seyla Talha Ahsan, Adel Abdul Bary and Khaled Al-Fawwaz – can also be extradited, while the case of a sixth man, Haroon Rashid Aswat, was adjourned today until a further hearing.
Today’s verdict declared that “detention conditions and length of sentences of five alleged terrorists would not amount to ill-treatment if they were extradited to the USA”.
The judges emphasised that today’s ruling only becomes final after three months, if there has been no further appeal.
Meanwhile, the judges said, “the court decided to continue its indication to the United Kingdom Government that the applicants should not be extradited until this judgment became final or until the case was referred to the Grand Chamber (of the Human Rights court)”.