A Sydney Uber driver accused of raping a woman who fell asleep in his car stopped at a service station to buy condoms before having what he says was "consent sex".

Muhammad Naveed, 41, has pleaded not guilty to having sexual intercourse without consent with a heavily intoxicated 22-year-old British nanny on a Saturday night in October 2015, when he picked her up in Kings Cross.

At the opening of the District Court trial on Tuesday, crown prosecutor James Trevallion said the woman had been drinking with friends at several venues and got into what she thought was a cab.

He said that en route to the eastern suburbs where the woman lived, Naveed pulled into a service station and bought condoms and a bottle of water, saying to her, "I've just got these".

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"She became confused ... and did not really understand why the accused was showing her this packet of condoms," Mr Trevallion said.

Naveed then drove in the opposite direction to the woman's home, stopped in a side street and asked if she wanted to move to the back seat, the prosecutor said.

"The complainant will tell you at this point she could not keep her eyes open and she was falling asleep," he told the jury.

The next thing the woman remembers is waking up to find Naveed on top of her.

"She did not have the strength to be able to push him off," Mr Trevallion said.

Afterwards, Naveed drove her home and she fell asleep on the way.

At home, the woman phoned a friend, who called police.