Footage posted on Twitter by @WildlifeCafe appeared to show a small handful of Metropolitan Police officers in high-visibility jackets dancing to music and responding to chants of "we love you" from supporters of the Extinction Rebellion action at Oxford Circus.
One officer could be seen applauding as the crowd began cheering while another raised his hand aloft in acknowledgement of their support.
Subsequent statements on the @WildlifeCafe account backed the officers, who were said to be in solidarity with the protesters.
But Scotland Yard said enquiries were being made to identify those involved.
Commander Jane Connors said: "I'm disappointed by the video and the unacceptable behaviour of the officers in it.
"We expect our officers to engage with protesters but clearly their actions fall short of the tone of the policing operation at a time when people are frustrated at the actions of the protesters.
"We will be reminding officers of their responsibilities and expectations in policing this operation - however the majority of officers have been working long hours and I am grateful to them for their continued commitment."
Pledging their support for the officers, the @WildlifeCafe said they had concerns the video would be misrepresented.
They wrote: "This clip was just a momentary bit of fun these officers had with the crowd nothing more.
"Climate catastrophe is the issue and solidarity with Extinction Rebellion."
The video came during a third day of protests in the capital, which saw scores of people arrested as roads and bridges were blocked while some activists disrupted rail services by gluing themselves to a train.