Radical Islamist cleric Abu Hamza has failed in a last-ditch High Court bid to halt his extradition from the UK to the US to stand trial on terrorism charges.
The judges also rejected legal challenges by Babar Ahmad, Syed Ahsan, Khaled Al-Fawwaz and Adel Abdul Bary, and said they should all be extradited immediately.
A Home Office spokesman said: "We welcome the High Court decision on Abu Hamza and others. We are now working to extradite these men as quickly as possible."
All five cases returned to the High Court after judges at the European Court of Human Rights refused to intervene and stop the Home Secretary extraditing them.
Between 1999 and 2006, the men were indicted on various terrorism charges in America.
Hamza has been charged with 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.
Ahmad, a computer expert from south London, and Ahsan are accused of offences including using a website to provide support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country.
They wanted their removal stopped so that they could challenge a decision by the Director of Public Prosecutions not to allow British businessman Karl Watkin, a campaigner against the UK's extradition arrangements with the United States, to bring prosecutions against them in the UK.
Bary and Al-Fawwaz were indicted - 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.