Rauf, who is of Pakistani origin, was arrested in August 2006, on a tip-off from British investigators.
He has been described as a key suspect in a purported plot to blow up aeroplanes flying from Britain to the United States which prompted a major security alert at airports worldwide and increased restrictions on carry-on items.
Rauf was arrested and charged in Pakistan with possessing chemicals that could be used in making explosives and for carrying forged travel documents.
The prosecution later withdrew the case against him, though he remained in jail awaiting a decision on a British extradition request against him.
Britain had asked Pakistan to hand him over in connection with a murder inquiry in Britain in 2002 which is separate from the alleged terrorism plot.
But Rauf's lawyer, Hashmat Habib, has sought to block the move, saying the two countries do not have an extradition treaty and that Rauf had been cleared of any terrorism charges.
Habib said on Saturday that his client had been brought to court in connection with the extradition proceedings, but said he had no knowledge of Rauf's escape.
Meanwhile, the British government this week denied media reports that Rauf was to be extradited from Pakistan as part of a secret deal involving the arrest in Britain of suspects wanted by Pakistan.
Two men accused of inciting terrorism and murder in Pakistan and of having links with an international terrorist group were detained in London on Tuesday.
Faiz Baluch, 25, and Hyrbyair Marri, 39, were arrested last week and jointly charged under Britain's Terrorism Act.
Both claim they are peaceful activists calling for the independence of Baluchistan, a troubled province of Pakistan.