Five terrorist suspects including radical preacher Abu Hamza can be extradited from the UK to America for trial, human rights judges have ruled.

The European Court of Human Rights in Strasbourg rejected the men's claims that 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.

The five include radical Muslim preacher Abu Hamza, currently serving a seven-year sentence in Britain for soliciting to murder and inciting racial hatred, and Babar Ahmad, a 36-year-old computer expert and alleged terrorism fundraiser who has been held in a UK prison without trial for nearly eight years.

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 until a further hearing.

The 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 human rights judges emphasised that the latest 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)".

The judges said that between 1999 and 2006 all six men were indicted on various terrorism charges in America. Hamza has been charged with 11 different counts of criminal conduct related to the taking of 16 hostages in Yemen in 1998, advocating violent jihad in Afghanistan in 2001 and conspiring to establish a jihad training camp in Bly, Oregon, between June 2000 and December 2001.

Ahmad's father, Ashfaq, said he and his family were "very disappointed" by the court's decision. "The fundamental question remains as to why this matter has even got to Strasbourg, and why Babar needs to be extradited to the US," he said. "There has been a serious abuse of process."

Home Secretary Theresa May said the Government "will work to ensure that the suspects are handed over to the US authorities as quickly as possible".

David Cameron hailed the decision, saying: "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."