His publicist, Max Clifford, said that, though Dewani's case would be heard again, he would eventually be sent to South Africa to be tried for the 2010 murder of his wife, Anni.
"Shrien will be detained until he is well enough to be sent to South Africa," Clifford said.
A judge of the High Court in London ruled on Friday that it would be "oppressive and cruel" to extradite Dewani before he was "fit and well".
A second man has come forward to claim that he has had sex with Dewani.
Britain's Daily Star reported yesterday that "a respected political aide who mixes in the highest circles at Westminster" said he had had sex with Dewani on several occasions in a private room at gay fetish club The Hoist, in London.
The paper said the 53-year-old political adviser had made a statement to Scotland Yard.
He reportedly claims to have first met Dewani at the club nine years ago, and that Dewani is a "submissive" who enjoys sado-masochism and dressing in leather.
Prosecutors claimed in the extradition hearing that Dewani had said he needed to "find a way out of getting married".
The case will return to the Westminster Magistrate's Court. Given that Dewani denies involvement in the murder, he will most probably plead "not guilty". The case will then be passed back to the High Court.
Dewani can still appeal to the UK Supreme Court and then the European Court of Justice.
Dewani is officially no longer a suicide risk and his physical and psychological health are said to be improving.
High Court judge Sir John Thomas explained at the hearing on Friday that "balancing his unfitness to plead, the risk of a deterioration in the appellant's condition, the increased prospects of a speedier recovery if he remains here [in Britain] and, to a much lesser degree, the risk of suicide and the lack of clear certainty as to what would happen to the appellant if returned in his present condition, we consider that on the evidence before the senior district judge it would be unjust and oppressive to order his extradition."
The other aspect of the original appeal, the conditions under which Dewani would be detained in South Africa, have been declared not to breach the European Convention on Human Rights and not a major threat to his safety.
Anni's family is convinced that extradition is the only way for justice to be served.
"We just want him to get better so that he can finally go to South Africa to tell us what happened," said a family spokesman.
Clifford said Dewani would remain in a mental-health clinic.
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