Home Office Minister Andy Burnham says suspects being extradited from Britain under new fast-track proceedings will remain absolutely protected from the death penalty or torture.
Mr Boudhiba is accused of helping al-Qaeda
He told the BBC that the UK government would not permit anyone it had surrendered to another European state to be sent on to a country which violated these human rights.
"We are absolutely clear on the point that the death penalty and torture are absolute bars to extradition.
"The Extradiction Act 2003 makes explicit the link with human rights. We have always set a great deal of store by these points and will absolutely continue to do so."
New arrest warrant
Mr Burnham was speaking to File On 4 which this week examined the cases of extradition prisoners currently held in the UK.
In one case, a solictor is pressing the Spanish Government for guarantees that his client, held in the UK for 14 months, will not be returned to his native Tunisia.
Hedi Boudhiba is accused by Spain of being part of a terrorist network linked to the 11 September attacks, the alleged ricin plot in Britain and the funding of fighters in Iraq.
Julian Hayes, who has prepared Mr Boudhiba's High Court Appeal, says the UK, US, Portuguese and German authorities had all interviewed him and decided not to prosecute him or seek his extradition.
Then Spanish authorities came to the UK and issued the new European Arrest Warrant when he refused to speak to them.
Mr Hayes says, "There's been a free flow of information between these authorities and the Spanish can easily obtain that information.
"We have no guarantees given to us by the Spanish authorities that he would be allowed to stay in their country.
Mr Boudhiba ran the risk of being placed in a Tunisian prison "where at the very least he'll be tortured and at the very worst he'll be killed."
No-one from the Spanish Government was available for interview.
Later this week, the case of the UK's longest-serving extradition prisoner returns to the High Court.
Algerian Rachid Ramda, 35, is accused by France of conspiring in an explosion which killed eight people in a Paris metro station in 1995, and of organising and financing several other bombings.
Eight people died in the Metro attack in 1995
Solicitors argue that a crucial confession implicating Mr Ramda was obtained through the brutal treatment of one of the bombers in police custody.
Mr Ramda has been held for almost a decade without trial, prompting the UK Government to introduce the streamlined extradition procedures.
Mr Burnham told File On 4: "The case has taken a long time, I think it does make the case for why the government changed the law with regards to extradition a couple of years ago."
Since the beginning of last year, any of the 25 European nations have been able to issue arrest warrants for extradition within the EU. They are supposed to take three weeks to come to court for the identity of the suspect to be checked.
The cases are then intended to move quickly through hearings before the suspects are sent to face their trial.
The aim is for terrorism suspects to meet speedy justice under the procedures. But critics argue that under the new law there is a conflict between efficiency and human rights.
File On 4: BBC Radio 4, Tuesday 11 August, 2005 at 2000 BST and repeated on Sunday 16 August, 2005 at 1700 BST.