Kazakhstan's JSC BTA Bank, formerly headed by Mukhtar Ablyazov but now nationalized, had sought an order requiring him to begin serving the sentence while pursuing an appeal.
Lord Justice Martin Moore-Bick ruled that, assuming Ablyazov declined to appear, such an order would have the effect of dismissing the appeal without a hearing on its merits.
Ablyazov dropped out of sight just before he was sentenced in London in February to 22 months in prison for contempt of court during a financial fraud trial. He is being sued by the bank, which is now nationalized, for allegedly stealing nearly $5 billion while he was chairman and part-owner.
Ablyazov's lawyers apparently don't know where he is, the judge said.
In 2009, the newly nationalized bank obtained a worldwide order freezing assets of Ablyazov and a number of companies he is believed to control. When Ablyazov failed to comply with the terms of the order, the bank successfully petitioned a British court to put many of the companies in the hands of receivers.
The court later ordered Ablyazov to disclose his assets and to remain in Britain until he complied.
A year ago, the bank sought a court order to put Ablyazov in prison for contempt, alleging more than 30 breaches of court orders.
"There are certainly strong grounds for believing that Mr. Ablyazov is in wilful and contumacious default of other orders of the court," Moore-Bick said.
"Much of what he says appears at first sight to be exaggerated and implausible and it is striking that the fears for his personal safety on which he now relies so heavily were voiced only after judgment was given in the committal proceedings," the judge added.
Moore-Bick commented that Ablyazov appeared to be abusing the process of the court.
"He has, for example, dealt with assets in breach of the freezing order and there is evidence to suggest that he is seeking to do so again. He has failed to co-operate with the receivers. There are very strong reasons for thinking that he has left the jurisdiction in breach of the court's order," the judge said.
Moore-Bick rejected Ablyazov's claim that he has no money to defend himself, but depends on third parties.
"There was good reason to believe that the company which is now said to be lending him funds to support the litigation, Green Life International S.A., is also owned or controlled by him," the judge said.
Ablyazov, a former energy minister in the Kazakh government, was a leader of an opposition movement, Democratic Choice. He was convicted of corruption and abuse of office in 2002 and sentenced to six years in prison and a heavy fine.
He was pardoned by President Nursultan Nazarbayev the following year, and dropped out of politics.