The European Court of Human Rights has ordered a halt to the extradition to the US on terror charges of radical cleric Abu Hamza al-Masri.
Abu Hamza, jailed in the UK for soliciting to murder and racial hatred, and three other British men complained about the length of sentence they may face if convicted in the US.
Their cases will be delayed for further submissions to the Strasbourg court.
The Home Office said that the men would remain in custody.
The US has sought to extradite Abu Hamza, the former head of Finsbury Park mosque in north London, since 2004, saying that he had attempted to set up a terrorism training camp in Oregon.
The three other men facing extradition are Babar Ahmad, Syed Ahsan and Haroon Rashid Aswat. Mr Ahmad and Mr Ahsan were allegedly involved in raising funds for exremists. Mr Aswat is accused in relation to the alleged terror camp.
In each case, the US has indicated that the men face very long sentences in a "supermax" prison in Colorado.
The four applicants argued that the length of sentences they faced and the conditions of the prison, ADX Florence, breached their human rights.
The European Court said judges wanted to see more detailed arguments on the prison conditions and the effect of the length of sentences.
In the case of Abu Hamza, the court said he had no case against the conditions at the prison because he would spend only a brief spell there because of his disabilities. Abu Hamza lost his hands in an explosion in Afghanistan and is partially blind.
The other men could face a form of solitary confinement that some critics have dubbed prolonged psychological torture.
The court said there should be further legal argument on whether life without parole at the prison would breach the suspects' human rights.
Two British courts have already approved the extraditions. Abu Hamza has served half of his seven-year sentence and is now being held under extradition law.
The UK government must submit further arguments to the court by 2 September about why it should be allowed to extradite the four.
In a press statement, Strasboug said: "The court considered that there was no reason to believe that the US government would breach the terms of its diplomatic assurances [not to designate the men enemy combatants].
"Nor did it consider that any of the applicants' claims in respect of their trials in the US Federal Courts… would amount to a flagrant denial of justice. Accordingly, those parts of the applicants' complaints were declared inadmissible."
But it said that the arguments over the length of the sentences that the men could face "raised serious questions".
Abu Hamza, Mr Ahmad and Mr Ahsan face life sentences and US prosecutors have said that Abu Hamza could be jailed for 100 years. Mr Aswat faces a maximum of 50 years.
UK Home Secretary Theresa May said: ""We note that the European Court of Human Rights has decided that all the applications are partly admissible. We await the court's judgement on the case. In the meantime these individuals will remain in custody."
A spokesman for Mr Ahmad said he was "very pleased" with the delay and that lawyers for the suspect were pressing the new government to allow him to be tried in the UK.