Britain vowed to hand over radical Muslim preacher Abu Hamza to the United States on terrorism charges as soon as possible after the European Court of Human Rights rejected his final appeal.

The court upheld an April 10 ruling against the hook-handed terror suspect and four others which had approved their extradition by London.

The suspects had argued that they would face degrading treatment because they would be sent to the notorious ADX supermax prison in Florence, Colorado and would face possible multiple life sentences.

But the Grand Chamber of the court unanimously decided there would be "no violation" of the European Convention of Human Rights if they were sent to the United States.

"Today the Grand Chamber Panel decided to reject the request. This means that the Chamber judgment of 10 April 2012 is now final," the court said in a statement.

The British government welcomed the decision, which comes after a lengthy legal battle that has dented the Conservative-led administration's claims to be tough on national security.

"The Home Secretary (interior minister Theresa May) welcomes today's decision not to refer the cases of Abu Hamza and four others to the Grand Chamber," a spokesman for the interior ministry said.

"We will work to ensure that the individuals are handed over to the US authorities as quickly as possible."

A British government source told AFP the extradition was "likely to be within weeks rather than days -- at least a couple of weeks for arrangements to be put in place".

Hamza lodged the appeal along with computer expert Babar Ahmad, who has been held in a British prison without trial for eight years after being accused of raising funds for terrorism.

The others to lose their appeals were Syed Tahla Ahsan, Adel Abdul Bary and Khaled Al-Fawwaz.

The court suspended judgment on a sixth man, Haroon Rashid Aswat, saying it required further consultations on his schizophrenia.

Abu Hamza, the former imam of the Finsbury Park mosque in north London, is wanted in the United States on charges including setting up an Al-Qaeda-style training camp for militants in the northwestern US state of Oregon.

He is also accused of having sent money and recruits to assist Afghanistan's hardline Taliban militia and Al-Qaeda, and of helping a gang of kidnappers in Yemen who abducted a 16-strong party of Western tourists in 1998.

Hamza, who is in his mid-50s and has one eye and a hook for one hand, was jailed in Britain for seven years in 2006 for inciting followers to murder non-believers.

Aswat was indicted as Hamza's co-conspirator while Bary and Al-Fawwaz were indicted with late Al-Qaeda leader 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.

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.