Qatada's legal team was challenging the court's decision that the 51-year-old could be sent back to Jordan with diplomatic assurances that he would not be tortured.
It is separate from the court's initial bar on deportation which required the Government to first get assurances from Jordan that evidence gained through torture would not be used against Qatada if he is sent back.
Repeated failed attempts by UK governments over the last 10 years to deport the radical cleric have cost nearly £1 million in legal fees, Government figures show.
Terror suspect Abu Qatada has lost his attempt to make a final deportation appeal to European judges.
The prospect of Abu Qatada being sent to Jordan for trial is getting closer but it could still be some months away.