Gregory Cox, 31, the founder and chief executive of the UK based Quintessential Finance Group, was charged in January after a 21-year-old Bermudan woman claimed he had raped her after meeting her in a nightclub.
The successful entrepreneur, who was educated at the £30,000 a year Millfield School in Somerset, has denied the allegations, claiming that the sex was consensual.
But at a preliminary hearing in Sydney, lawyers for the businessman argued that his high profile meant his identity should be kept out of the media in the build up to any trial.
Mr Cox's barrister, Graham Turnbull, told the Downing Centre Local Court that his client had been to an "elite" school and came from a well known family.
He told the court that since the allegations had been made public, Mr Cox had been subjected to "an undue level of interest" and "significant inconvenience".
Mr Turnbull told magistrates that the case could cause further "unwarranted hardship" if it was sent to trial and applied for Mr Cox to be granted anonymity.
But magistrate Glenn Walsh threw out the application saying he had been presented with "nothing out of the ordinary" to justify the move.
The hearing also addressed whether the alleged victim could be forced to give evidence at a committal hearing, when a magistrate will decide whether Mr Cox should stand trial.
The court heard how Mr Cox had met the woman at the popular Bucket List nightclub close to Bondi on January 22 and is accused of raping her between 11.10pm and 11.30pm that night.
Mr Cox has admitted having sex with the woman, but has denied rape, claiming the intercourse was consensual.
The court heard how two people took the woman to a police station within minutes of the incident and that she was later found to be suffering from a head injury, although that could have been up to two days old.
Prosecutor Claire Moore said several aspects of the woman's story was backed up by "corroborating evidence".
But Mr Turnbull told the court that his client had been "open" with police throughout the investigation.
Mr Cox, who has a £1 million flat in Battersea, south London, was understood to be in Sydney with a colleague attending a digital marketing conference, when the alleged attack took place.
Following his arrest he was ordered to hand over his passport and has had to post a £68,000 bail surety.
In recent months he has been staying at a luxury beachside apartment in the suburb of Bronte, a few miles from Bondi.
On the Quintessential company website, Mr Cox is described as an entrepreneur with more than 12 years experience running his own company, from start-up to £40 million.