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Dewani, whose extradition hearing starts on Monday, also allegedly paid to have sex with another man.
According to the UK's Sun newspaper, Anni sent several distressed messages to her sister, complaining about his refusal to sleep with her on their wedding night in India.
Anni was murdered in what was allegedly made up to be a failed hijacking in Gugulethu in Cape Town, while the couple was on their honeymoon in November last year.
She was found dead with a bullet wound in the neck.
Dewani was arrested after the driver of the vehicle, Zola Tongo, told a court that Dewani had asked him to hire hit men to kill Anni.
The Sun reported yesterday that Dewani did not sleep with his 28-year-old bride before marriage or on their wedding night in Mumbai.
A BBC Channel 4 programme was set to reveal last night that Anni "cried herself to sleep alone on a sofa on their wedding day following a blazing row".
Anni's sister, Ami Denborg, admitted she thought Dewani's pre-marriage sex ban was "strange", but says the family assumed he was just being a good Hindu, reported the Sun.
Meanwhile the National Prosecution Authority is confident that the UK court will send him to face trial in South Africa, though one of the hitmen allegedly hired to kill Anni is on his death-bed.
Tongo's lawyer, William da Grass, said there were concerns that Xolile Mngeni, who had an operation to remove a brain tumour, "is not going to recover".
Mngeni and Mziwamadoda Qwaba were the alleged triggermen hired to commit the killing.
"All I have heard is that there are grave concerns about his recovery," said Da Grass.
NPA spokesperson Mthunzi Mhaga said the UK's court's decision not to relax Dewani's bail conditions was an indication that he would be brought back to South African to face trial.
"We've complied with legislative requirements as far as the paperwork is concerned and even during the hearing we put up a very strong case in favour of his extradition and we believe strongly that he will be extradited," Mhaga said.