PC Daryl Marley, 32, of Newport Street, Milton Keynes, Buckinghamshire, called Grace Shearman a f****** slag in Simmons bar, Soho, last October 29, shortly after they broke up.
Marley, who was off-duty, then threatened to punch Ms Shearman's colleague Tom Evans, who said the defendant was aggressive, “tensed up" and in a “fighting stance".
On Thursday, the force said misconduct proceedings would begin against PC Marley, who is suspended, after he was ordered to pay £1,000 at Westminster Magistrates’ Court for common assault.
At an earlier court hearing on Monday, District Judge King said: “You were angry, annoyed and upset."
“You will likely lose your job, but anybody acting in public service is understandably held to a higher standard."
The court heard how Ms Shearman was attending a Met colleague's leaving do when Marley approached her, saying he said, “I've always known you were a f****** slag".
She told the court: “It was embarrassing that it was in front of my colleagues from work and it made me feel worried about what he could do if he could do that in front of a load of people."
Marley said he probably had a “bit too much" to drink and got emotional when he saw her.
He claimed to have told her “glad you're having a good night you f****** slag".
The officer added: “I am truly sorry I said that to Grace and wish to apologise for my conduct, which was inappropriate and unacceptable."
Mr Evans said Marley approached Ms Shearman 10 minutes after making the comments, and he stepped in to prevent the situation escalating.
He told the court: “(Marley) put his arm on my right shoulder and whispered into my ear: 'I know you're following her, you little f****** creep"'.
Mr Evans said he asked Marley: "What the f*** did you just say to me?"
The defendant allegedly replied: “I'll f****** knock you out, you c***".
Mr Evans said: "I felt like he was going to approach me and punch me. It was the aggression in his voice and the look on his face. He was tensed up. He looked as if he was going into a fighting stance."
He said Marley was held back by people in the bar before security intervened.
However, Marley, who told the court he is a “proud" police officer, said he never threatened Mr Evans.
He said he had instead told Mr Evans: “Go and sleep in your car, you prick".
The judge dismissed an earlier charge of using threatening, abusive, insulting words or behaviour to cause harassment, alarm or distress, saying Marley's words to Ms Shearman, saying they had not reached the required threshold.