A British judge on Monday set the murder suspect's extradition hearing for July after hearing that Dewani is now a "husk" of a man who suffers flashbacks of the night his bride was killed.
Dewani, who is being treated at a psychiatric hospital for depression and post-traumatic stress disorder, had his extradition halted in March on mental health grounds, and a judge ruled Monday that he needs several more months to recover.
His 28-year-old wife Anni, a Swede of Indian origin, was shot dead in November 2010 during an apparent car hijacking in Cape Town just two weeks after the Hindu couple's wedding.
Her family voiced their frustration at the further delay, saying the wait would be "eight months of torture" for them.
"We accept the court's decision," her uncle Ashok Hindocha told reporters outside court.
"We know these things take time, and British justice has taken too much time.
"We have no choice. What can we do?
"We would like to thank the people of South Africa and the United Kingdom. Thousands of letters are still coming in," he added.
He and Anni Dewani's father Vinod Hindocha were travelling to South Africa to "ensure justice is being done", he said.
After hearing evidence from his psychiatrist, Chief Magistrate Howard Riddle bailed the British businessman until a review hearing on April 11th.
A five-day full extradition hearing will follow from July 1st if the 32-year-old recovers to a point where he is deemed fit to stand trial.
Dewani, who denies orchestrating the murder, was not present for the hearing at Westminster Magistrates Court in central London.
A South African man was found guilty of the murder last month and two other local men were jailed over the killing say Shrien Dewani ordered the hit.
Dewani's lawyer Clare Montgomery told the court her client was now a "husk of a man" due to his mental condition.
Citing medical reports, she said Dewani's illness had become increasingly disabling. He is "very withdrawn" and had voiced frustration over poor concentration, while his sleeping pattern was erratic.
The lawyer said he also has a phobia of going out, is frightened of being in a moving car and does not even want to go on visits home.
"He cannot travel by car as he has a severe reaction," she said. "He doesn't even want to go to the shops on his own.
"In his current state it is unthinkable he would be able to plan any escape, let alone effect one," she added.
Dewani's psychiatrist Paul Cantrell told the court his patient was still suffering from severe depression and post-traumatic stress disorder, with extreme sensitivity to noise and smells among the chief symptoms.
"Something akin to the smell of the breath of the man who, by his account, was holding the gun to his head" would "trigger the re-experiencing of things in South Africa", he said, explaining: "It is as if he was there".
"He remains exceedingly unwell."
Hugo Keith, representing the South African authorities, said the case could not be "adjourned indefinitely".
Both sides agreed that a change to a quieter mental hospital in his native Bristol, southwest England, might aid Dewani's recovery.
His £250,000 ($400,000) bail security remains and police will retain his passport.