The Government could still apply directly to the Supreme Court in a bid to take the case further.
The normal process is to submit a permission to appeal application which would then be considered by three Supreme Court justices.
They would decide whether or not the application raised a point of law of general public importance.
We are disappointed with the Court of Appeal's decision but will now request permission to appeal directly from the Supreme Court.
The Government remains committed to deporting this dangerous man and we continue to work with the Jordanians to address the outstanding legal issues preventing deportation.
The Home Secretary pinned her hopes for ousting Abu Qatada from Britain on a fresh deal with the Jordanians.
A Tory MP and former government lawyer give their view on the UK potentially withdrawing from the ECHR to aid Abu Qatada's deportation.
The Government has been refused permission to take its fight to remove preacher Abu Qatada from the UK to the Supreme Court.