A MILLIONAIRE British entrepreneur accused of raping a woman on Bondi Beach has fought to keep his identity secret because his privileged background meant he would be subject to "undue embarrassment".

A magistrate was yesterday told the allegations had already caused Gregory Charles Cox, 31, the CEO and founder of the UK-based Quintessential Finance Group, "significant inconvenience" and the case could cause further "unwarranted hardship" if he was sent to trial.

He was charged in January with raping a 21-year-old Bermuda woman he had just met at Bondi's The Bucket List bar. Cox claims the sex was consensual.

His lawyer, top silk Graham Turnbull SC, told Downing Centre Local Court his client had been to an "elite" school, came from a well-known family and was renowned for his exploits on the football field - which had exposed him to "an undue level of interest" since the allegations were made public.

Cox, who is living in Bronte after having his passport confiscated, attended the exclusive Millfield boarding school in the lush UK countryside, which lists Arabian princes and numerous politicians among its alumni.

Yesterday he faced a hearing to decide if the alleged victim could be forced to give evidence at his committal hearing, when a magistrate will rule if he stands trial.

Mr Turnbull tried to have Cox's identity suppressed in the media but magistrate Glenn Walsh threw out the application saying he had been presented with "nothing out of the ordinary" to justify the move.

The court was yesterday told Cox freely admitted to having sex with the woman and the key issue in the case was her consent.

The court heard two people took the woman to a police station within minutes of the incident and that she was later found to be suffering a head injury, although this could have been up to two days old.

Prosecutor Claire Moore said several aspects of the woman's version of events were backed up by corroborating evidence. Mr Turnbull said Cox had been "open" with police. The hearing continues next month.