Muhammad Naveed, 41, is on trial in the Downing Centre District Court accused of raping the woman, then 22, after he picked her up near The World Bar in Kings Cross in the early hours of October 18, 2015.

In his opening address, Crown prosecutor James Trevallion told the jury he expected the woman would give evidence that Mr Naveed helped her into the back of his car and she later woke up and found him on top of her.

Mr Naveed has pleaded not guilty, and the court heard that, in an interview with police, he claimed he had asked the woman if she wanted to have sex and she agreed.

Mr Trevallion said the woman had recently arrived in Australia from Britain and was working as a nanny for a family in Sydney's eastern suburbs when she was allegedly attacked.

The woman, who cannot be identified for legal reasons, had been drinking throughout the day and evening with a group of friends at Randwick Racecourse, Star City Casino and Scruffy Murphys before they decided to go to The World Bar.

When they reached the front of the queue to the bar, the woman decided she did not want to pay the cover charge to enter and told her friends she would get a taxi home.

Mr Trevallion said he expected the woman would give evidence that she was intoxicated and her memory of what unfolded that evening and early the next morning were partial and fragmented.

"What she does remember is being in what she believed was a taxi," Mr Trevallion said. "She doesn't recall how she got into the taxi. She just remembers being in this vehicle and travelling, she believed, back towards her home."

The court heard that Mr Naveed stopped to buy condoms and water from a service station in Rushcutters Bay before he returned to the car and told the woman: "I've got these."

The woman is expected to give evidence that Mr Naveed asked her if she wanted to get into the back seat of the car and she thought it was because she was falling asleep and could not keep herself upright.

"I expect she will tell you the accused helped her into the back seat of the car and she fell asleep," Mr Trevallion said.

When the woman woke up she realised the accused was having sex with her and she struggled to push him away and tried to tell him to get off her.

"The Crown case is the accused continued to have sexual intercourse with the complainant for around about two minutes," Mr Trevallion said.

Mr Naveed then allegedly returned to the driver's seat, and the next thing the woman says she remembers is arriving at the eastern suburbs property where she was staying.

The court heard the woman did not pay, nor was asked to pay, for the trip and she immediately told a friend what had happened and police were called.

A pharmacologist is expected to give evidence during the trial that, when the alleged rape occurred, the woman would have had an estimated blood alcohol concentration of 0.231.

The Crown will contend Mr Naveed knew the woman had not given her consent to have sex with him and, moreover, that she was too drunk to be able to give consent.

The defence was not expected to give an opening address. The trial continues.