The pair have applied to the European Court of Human Rights after claiming MI5 was complicit in their torture by Pakistani security services, a claim that has already been rejected by British courts.
Officials at the European Court have allowed their application to go ahead rather than declaring it inadmissible, as they do with thousands of cases a year.
The Government must now respond to the claims, and if its explanation does not satisfy the court it will order a full hearing which, if successful, would almost certainly lead to the British courts being forced to quash the convictions.
The new development raises further questions about the influence of Strasbourg over British sovereignty, and the way human rights legislation is being exploited by defence lawyers.
The unique case means European judges will have to decide on a point of fact - whether the pair were tortured with the complicity of British security forces - rather than on a point of procedure, which is what the Strasbourg court has been concerned with until now.
A leading barrister said Strasbourg's interference in the case already amounted to a significant and "unacceptable" departure by European judges by considering issues that should be left to British courts to decide.
The Sunday Telegraph's campaign, End the Human Rights Farce, has highlighted scores of cases in which criminals have exploited human rights laws.
Lord Carlile, the QC who until last year served as the Government's independent reviewer of terrorism legislation, said: "To have the European Court of Human Rights intervening in judgments of fact - as opposed to judgments of law - really would be a new departure and, in my view, a completely unacceptable departure.
"In my view, findings of fact are not for an international court to determine, otherwise instead of the 150,000 cases currently awaiting judgment at Strasbourg there would be 550,000 or more. It is another illustration of the need for a fresh look at the way the European Court operates in relation to British proceedings."
Lord Carlile said that if the case went ahead he believed it would be the first time terrorist convictions had been challenged at Strasbourg in this way.
In a separate case, three of the failed July 21, 2005, bombers are also challenging their convictions at Strasbourg on a point of law rather than of fact.
One of the extremists in the latest case, Salahuddin Amin, was jailed for life in 2007 for his role in a terrorist cell that conspired to detonate a massive fertiliser-based bomb at Bluewater shopping centre in Kent or at London's Ministry of Sound nightclub.
Amin's lawyers allege the British authorities knew that incriminating evidence against him had been obtained through torture. He claims MI5 were complicit in his torture by Pakistani security agents, whom he alleges used pliers to remove three of his fingernails.
The second convicted terrorist, Rangzieb Ahmed, is the highest ranking member of al-Qaeda yet to be put on trial in Britain. Ahmed, 37, was at the centre of al-Qaeda's global web and had links with every British terrorist cell including the July 7 and July 21 plotters. The first person to be convicted of "directing terrorism", he alleges MI5 allowed him to leave Britain for Pakistan and tipped off intelligence services there so that he could be arrested in 2006 and tortured. Ahmed claims Britain was complicit in his torture.
He also claims he was denied a fair trial because it was "informed by the interrogation undertaken in Pakistan" and he was denied access to material after a public interest immunity certificate was granted in the case.
Amin was one of five men jailed for the fertiliser bomb plot who were described by the trial judge, Mr Justice Astill, as "ruthless misfits who should be removed from society for its own protection".
The cell, led by Omar Khyam, purchased ammonium nitrate fertiliser in November 2003. The amount - capable of bringing down a large building - was enough to be spread on an area equivalent to five football pitches, but co-conspirator Anthony Garcia told an agricultural merchant it was for his allotment. The gang moved the fertiliser to a self-storage facility near Heathrow, where police secretly switched it for cat litter.
The trial at the Old Bailey heard Amin had obtained detonators and provided the fertiliser bomb formula.
In paperwork submitted to the European Court Amin claims his right to a fair trial was breached because information against him was "obtained through the use of torture and inhuman and degrading treatment". He claims relevant material was withheld from him and that the trial judge mishandled how information should be disclosed to his defence team.
He also claims British authorities failed to carry out an effective investigation into his allegations of torture and ill-treatment, in breach of Article 3 of the European Convention on Human Rights.
Amin's fellow applicant to Strasbourg, Ahmed, who was born in Rochdale, Lancs, travelled to Dubai as part of an al-Qaeda cell in 2005, unaware that he was under surveillance. His luggage was secretly searched during the trip and found to contain notebooks with details of al-Qaeda contacts written in invisible ink. On his return, British security services continued to watch Ahmed and bugged his car.
David Davis, a former shadow home secretary, has said there was "hard evidence" of torture in the men's cases and there should be an inquiry.
He said: "British intelligence officers would have had to have been wilfully blind and deaf not to know what was going on." But in 2010 Baroness Scotland, the then attorney general, rejected a call for Scotland Yard to investigate the claims. Even though their cases have already been reviewed by the Court of Appeal in London, which declared their convictions safe, their lawyers applied to Strasbourg.
Officials at the European Court have now told the British authorities they must respond to claims that the men's human rights were breached during their prosecutions. It means the British taxpayer will foot further legal bills which are already estimated to have cost hundreds of thousands of pounds.
The European Court is expected to decide later in the year whether there will be a full hearing in the case of Ahmed and Amin, who are both British citizens.
A Foreign Office spokesman said: "We do not comment on ongoing legal cases."