The 33-year-old was working with the Met's Sexual Offences, Exploitation and Child Abuse Command when she was sent to take the victim's fingerprints and they kissed.
Over the course of the following month the pair met for sex four times, with one encounter taking place at the woman's grandfather's house on 24 February last year.
But the affair was exposed on 14 March when the rape victim told staff at the refuge where she was staying that she was "tired of being her dirty little secret".
Prosecutor Kate Bex said of her arrest and subsequent charges, according to The Sun: "The fallout from that disclosure was inevitable. Staff told her they were obliged to report it. The victim withdrew what she had said to the staff member, then asserting it had been attention-seeking lies."
The victim said she had fallen "in love" with Peters but the officer had refused to leave her partner, according to reports.
Peters, from Luton, joined the police in 2006 but her time in the force came to an end after she was arrested on 17 March, suspended from duty on 21 March and charged with misconduct in public office on 11 October. She was jailed for 22 months at Southwark Crown Court in December 2016 after admitting the charge.
Peters, who was a Sexual Offences Investigative Techniques (SOIT) officer, mouthed "I love you" to her partner as she was imprisoned.
At the Metropolitan Police misconduct hearing Peters' commanding officer, Detective Chief Superintendent Ivan Balhatchet, said she was "a popular member of her team" who had a "promising career ahead of her" before her dismissal.
Assistant Commissioner Martin Hewitt said Peters' conviction for misconduct "seriously undermines public confidence in the police".
He said: "Having considered the matter fully, and having regard to the nature and severity of the breaches of the standards of professional behaviour, my decision is that PC Peters is dismissed without notice."
Temporary Deputy Assistant Commissioner Richard Martin, in charge of professionalism, said in a statement: "The public and the Met expect police officers to behave with the utmost professionalism. It was PC Peters' job to protect those she was entrusted to help.
"She clearly abused her position by starting a relationship with the person she was there to support, when that person was at their most vulnerable.
"Such behaviour only damages the public's trust and confidence in the police and is completely unacceptable."
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