PC Rupert Edwards, 30, went to bed consensually with both women but went on to attack them later in the evenings after consent had been withdrawn, it is said.
Edwards, who was based in Twickenham, denies two counts of rape.
The officer met the first alleged victim on a night out in Richmond in August last year, and they slept together after taking a taxi to her home.
Prosecutor Robert Brown said the woman “remembered kissing” Edwards in the bar during the evening, and they headed home together at 3am.
After consensual sex, she “was tired and felt too sore for any further sex” and told Edwards: “I can’t go again”.
“The defendant pulled her leg over and then penetrated her....from behind”, said Mr Brown.
“(She) did not say anything further to him but she is clear that she did not consent to this, and that the defendant knew that she did not and carried on regardless.”
The woman said she “froze” during the alleged attack and afterwards “tried to put the incident out of her mind and get on with her life”, the court heard. But ultimately she reported Edwards in November last year.
The second alleged attack happened after Edwards met the woman on a night out in Wandsworth in September 2022 - 11 days after the first alleged rape.
She agreed to accompany him home but refused to have sex as they did not have a condom, the court heard.
“The defendant agreed to this and they were happy to do other sexual acts”, said the prosecutor. “(She) eventually went to sleep but was awoken by the defendant who had penetrated her vagina with his penis.
“She asked him what he was doing and told him to leave. The defendant apologized and left.
“(She) said that she was angry and confused because he had told her that he was a police officer and so she sent him a text message at 4.51am thanking him for destroying her faith in the justice system.
“At 4.59am she then called 999 and reported the matter to the police.”
When questioned, Edwards, who lives in Ashtead in Surrey, denied rape and insists both encounters were entirely consensual. He said the first woman had agreed to have sex throughout, and insisted the second woman had not refused to have sex without a condom and had not been asleep during their sexual encounter.
Judge Usha Karu KC, the Recorder of Southwark, told jurors to focus on the evidence during the trial.
“This defendant is and was a serving police officer in the Metropolitan Police Service”, she said. “There has been some considerable publicity about police officers and investigations – do not let any of that affect your judgment of the evidence in this case.”
The trial continues.