Domenico Rancadore is wanted in Italy to serve a seven-year jail term for his role in the Sicilian mafia and authorities are seeking his extradition.
The High Court decision was postponed from Wednesday when the 64-year-old former fugitive was taken to hospital with heart problems.
Judge John Goldring said it was clear that Rancadore had heart trouble, which should be borne in mind.
But there was "a real risk — indeed a very real risk — that he would abscond if granted bail", he said.
"In my view this appeal should be allowed and Mr Rancadore remanded in custody."
Known in the mafia as "The Professor", Rancadore had been on Rome's list of most dangerous criminals.
He had been living in a modest suburban house in west London under the name of Marc Skinner, with his English wife and children, when he was arrested on August 8th this year.
He was granted bail at Westminster Magistrates Court in London on Monday. However, he was not released after prosecutors issued notice to lodge an appeal.
Prosecutors told an earlier court hearing in August that Rancadore was a leader in a gang that "spread terror" on the Italian island of Sicily, "systematically murdering anybody who did not comply with the will of the members of the organisation".
Rancadore suffers from high blood pressure, angina and reflux, that court was told.
Rancadore was convicted in his absence of Mafia links in Italy after he went on the run and moved to Britain in 1993.