RADICAL preacher Abu Hamza and four other terrorist suspects wanted by US authorities will be handed over "as quickly as possible", Home Secretary Theresa May has said.

She gave her reaction after human rights judges ruled there would be no violation of the European Human Rights Convention if the UK extradited the five to the US to face terrorist charges.

However, the judges warned the Government not to extradite any of the men until a three-month deadline for a final appeal has expired.

The men had claimed the prospect of solitary confinement in a so-called "supermax" high-security jail and sentences of life imprisonment without parole would breach a European ban on "torture or inhuman or degrading treatment or punishment".

The ruling, after a series of controversial human rights judgments against the Government, was welcomed by Prime Minister David Cameron. He said: "It is right we have proper legal processes, although sometimes one can get frustrated with how long they take."

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

The ruling amounts to a first green light for US top security prisons, and the right of European governments to approve US extradition requests for high-risk suspects.

The verdict concerned five men including 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 – Syed 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 to consider the state of his mental health.

The verdict said "detention conditions and length of sentences of five alleged terrorists would not amount to ill-treatment if they were extradited".

The unanimous judgment said there would be no human rights breach either as a result of likely detention in ADX Florence "supermax" prison in Colorado, or the length of possible sentences on conviction.

Hamza faces charges in the US on 11 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.

Aswat was indicted as Hamza's "co-conspirator", while Bary and al Fawwaz were indicted, along with Osama bin Laden and 20 others, for their alleged involvement in, or support for, the bombing of US embassies in Nairobi and Dar es Salaam in 1998. Al Fawwaz faces more than 269 counts of murder.

Ahmad and Ahsan are accused of offences including providing support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country.

The judges acknowledged that, in the US, Bary faced 269 mandatory sentences of life imprisonment without the possibility of parole, while Ahmad, Ahsan, Hamza and Al-Fawwaz faced "discretionary" life sentences.

The judges said: "Having regard to the seriousness of the offences in question, the court did not consider that these sentences were grossly disproportionate or amounted to inhuman or degrading treatment."

They said "supermax" jail inmates, albeit confined to cells for the "vast majority" of their time, were provided with services and activities which went "beyond what was provided in most prisons in Europe".

A US embassy spokeswoman said: "The United States is pleased with the finding of the court regarding defendants Babar Ahmad, Syed Ahsan, Mustafa Kamal Mustafa (Abu Hamza), Adel Bary and Khaled Al-Fawwaz. We look forward to the court's decision becoming final and to the extradition of these defendants to stand trial."

Babar Ahmad's sister, former GP and mother-of-four Amna Ahmad, 33, vowed to fight his extradition "to the end".

She said: "He is obviously very, very disappointed with the ruling but it's added more fuel for us to pursue the British Government to ask what's gone wrong because we believe there has been a serious abuse of process.

"We're asking for rights that apply to paedophiles and rapists. They're afforded the chance to have a fair trial in the UK in front of a jury of their peers.

"Babar's not been awarded that opportunity."