Qatada is wanted by Jordan to face terrorism charges. British governments have for years tried to get rid of the cleric, who has been in and out of jail for a decade since first being arrested in 2001 and is currently on bail under tight restrictions which include a 16-hour curfew.
He argues his trial in Jordan might be skewed by evidence obtained using torture, despite a 2005 deal struck between Britain and Jordan which gives diplomatic assurances about his treatment and guarantees that court hearings would be fair.
In a setback to British Home Secretary (interior minister) Theresa May, who has denounced successive legal blocks to his deportation, judges at a special court in London which deals with security cases, ruled in his favour last month.
May has now submitted papers at London's Court of Appeal challenging that decision, the Home Office said. However, the appeal can only relate to a point of law and not the actual details of the case.
Jordan convicted Qatada in his absence of encouraging militants there who planned bomb attacks in 1999 and 2000. Under Jordan's 2005 deal with Britain, however, he would have a retrial.
The cleric, a Jordanian of Palestinian origin, was once described by a Spanish judge as "Osama bin Laden's right-hand man in Europe". Britain says videos of his sermons influenced Mohammed Atta, the ringleader of the September 11, 2001 attacks on the United States.