The European Court of Human Rights on Tuesday ruled that Britain can extradite five terrorism suspects to the United States to face charges that include life sentences in a maximum-security prison.

The court, based in the French city of Strasbourg, had been considering the cases of six people indicted in the U.S. between 1999 and 2006 on terrorism charges related to hostage-taking in Yemen and attacks on U.S. embassies in Africa.

The extradition of five suspects was approved by the court, including Abu Hamza, a radical Muslim cleric and a highly recognizable extremist in Britain. The case of the sixth suspect, Harron Rashid Aswat, was put off awaiting further information about his medical condition.

The suspects had argued they could face tough prison conditions and jail terms in the U.S. which could be in breach of the European human rights code, but the claim was rejected by the court on Tuesday.

"Detention conditions and length of sentences of five alleged terrorists would not amount to ill-treatment if they were extradited to the U.S.," according to the ruling.

The ruling added the five suspects should not be extradited until all court procedures had been exhausted.

British Prime Minister David Cameron said he was "very pleased" with the ruling, while home secretary Theresa May said the suspects would be handed over to U.S. authorities as quickly as possible.