The British government will try to speed up the extradition process after an eight-year legal battle to send radical preacher Abu Hamza to the United States, Prime Minister David Cameron said Saturday.

Abu Hamza and four other terror suspects were flown out of Britain overnight to the United States, just hours after the High Court in London threw out the men's final appeal against their removal.

"I'm absolutely delighted that Abu Hamza is now out of this country," Cameron said.

"Like the rest of the public I'm sick to the back teeth of people who come here, threaten our country, who stay at vast expense to the taxpayer and we can't get rid of them."

The United States first requested Abu Hamza's extradition in 2004 and it was approved in 2008 but the case then spent another four years in the European Court of Human Rights.

Cameron said the British government must "learn every lesson" from the saga.

"How do we stop these people coming in? How do we get rid of them more quickly? How do we make sure they don't spend so long at taxpayers' expense?" Cameron said.

Home Secretary Theresa May echoed his comments.

"It is right to look at the process. It is frustrating, I think everybody is frustrated at how long it has taken to extradite these particular individuals," she told BBC Radio.

"We will look very carefully at the comments that have been made by the Lord Chief Justice and look seriously at this whole process and whether there are too many stages in these processes.

"I think we do need to make some changes."

Abu Hamza was expected to make his first appearance in a US court later Saturday.

The former imam of the hardline Finsbury Park mosque in north London, Abu Hamza 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 sending money and recruits to Afghanistan's Taliban and Al-Qaeda, and of helping kidnappers in Yemen who abducted a party of Western tourists in 1998.

The extradition process for some of the other suspects was even longer.

Khaled Al-Fawwaz and Adel Abdul Bary, wanted on suspicion of involvement in 1998 attacks by Al-Qaeda on US embassies in east Africa, have been in jail in Britain since 1999 fighting extradition.

Babar Ahmad and Syed Tahla Ahsan, who are accused of operating a jihadist website, have been in prison without trial since 2004 and 2006 respectively.