Radical Muslim cleric Abu Hamza al-Masri lost a court battle on Friday to block his extradition to the United States where he faces terrorism-related charges.
He had said the extradition request was founded on evidence obtained by torture.
His lawyers argued that to send him to the United States to face charges dating back to 2000 would be "unjust and oppressive" because of the length of time that has passed since then.
In dismissing the challenge, Igor Judge said: "The 2003 Extradition Act must be applied and our extradition commitments honoured."
Hamza, who is serving a 7-year jail term in Britain for inciting his followers to murder non-believers, is accused of attempting to set up a terrorist training camp in Bly, Oregon, from 1999 to early 2000.
The Egyptian-born cleric, who applauded the September 11 attacks on New York and Washington in 2001, also faces charges that he was involved in plotting the seizure of 16 Western hostages in Yemen in 1998.
Four of the hostages, three Britons and an Australian, were killed when Yemeni troops stormed the militants' hide-out.
Police say his mosque in London had acted as a base for militants.
