Terror suspect Abu Qatada's lawyers will claim Jordan's assurances that evidence gained through torture will not be used against him are not good enough for him to be sent back.
The radical cleric, described by a judge as Osama bin Laden's right-hand man in Europe, is facing a retrial on terror charges after Home Secretary Theresa May was given the assurances by Jordan.
But the 51-year-old, who has challenged and ultimately thwarted every attempt by the Government over the last decade to put him on a plane, is fighting against deportation at a seven-day immigration tribunal appeal in central London.
Even if Qatada loses when the decision is handed down next month, it could still be many months before the Government can send him to Jordan as he could appeal again to Europe's human rights judges, his lawyers have said.
Qatada, who is in custody, is not expected to attend the hearing at the Special Immigration Appeals Commission (Siac), where Siac president Mr Justice Mitting, Upper Tribunal Judge Peter Lane and Dame Denise Holt will hear his appeal.
Repeated failed attempts by UK governments over the last 10 years to deport Qatada have cost nearly £1 million in legal fees, Government figures show.
No figures have been given for how much Qatada has received in legal aid and some estimates put the cost of keeping Qatada in the UK, either in a high-security jail or closely monitored under strict conditions in the community, along with the legal costs of the fight to deport him, at more than £3 million.
Edward Fitzgerald QC, representing Qatada, has said the cleric has now been in detention for seven years - "the longest period of administrative detention as far as we know in modern English history".
He was last refused bail over the Olympics, when police and security services were fully stretched, with judges also ruling that the risk of him absconding in the run-up to today's hearing justified his continued detention.
At the High Court in August, Lord Justice Hughes and Mr Justice Silber said they did not agree with Mr Fitzgerald's "gloomy prognosis that another year or more of litigation is to be expected after the fortnight's hearing in Siac".
Qatada could appeal against the Siac ruling, the judges said, but any appeal "would have to be on points of law" and it was not "an inevitability" that the European Court of Human Rights in Strasbourg would want to hear the case again.
Qatada, who is said to have wide and high-level support among extremists, was convicted in his absence in Jordan of involvement with terror attacks in 1998 and faces a retrial in his home country.
He also featured in hate sermons found on videos in the flat of one of the September 11 bombers.