Police community support officer (PCSO) Maya Hadzhipetkova was filmed telling Harmonie London, a 20-year-old singer with more than 320,000 YouTube subscribers, to stop performing on the street, telling her: "No miss, you're not allowed to sing church songs outside of church grounds, by the way."
The singer filmed some of the exchange and posted it to Instagram on Sunday. As the officer walked away, she is seen turning back and sticking her tongue out.
Ms London often performs worship music on Oxford Street.
A Met Police spokesman said: "We're reviewing body worn video of this interaction - it's more than 40 minutes long."
They added that the officer "knows she could have handled this differently and is speaking to her manager".
Footage of the conversation went viral online and the Met said it was "aware of significant social media commentary", adding that "some of the comments are personal and hurtful. This is unacceptable".
Former police officer Norman Brennan said the footage was "not a good look" and would not help the police regain public confidence while former Tory minister Ann Widdecombe called for the constable to be "struck off".
The Met said the 30 second clip was from a "43 minute conversation where the wider context is not immediately obvious".
Scotland Yard added: "Unlicensed busking is an ongoing issue in Westminster and during the interaction, the officer and her colleagues explained the busking legislation a number of times.
"They clarified the breach was due to the busking itself, rather than anything to do with the songs being sung.
"The officer was mistaken in saying church songs cannot be sung outside of church grounds."We’re sorry for the offence caused and will take the learning forward."