The footage depicts a cardboard effigy of Grenfell Tower - complete with figures at the windows - being burnt.
The crowd of people could be heard shouting "stay in your flat" and "help me, help me" as the Grenfell Tower effigy went up in flames.
Further in the video, one voice says: "That's what happens when they don't pay their rent", then another says, "All the little ninjas getting it".
Three officers carried evidence bags into the terraced property and knocked on neighbours' doors while the men were being questioned on suspicion of a public order offence.
British Prime Minister Theresa May tweeted Monday night about the effigy, calling it "utterly unacceptable".
In the recording, onlookers can be heard saying: "Help me!"
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In the video, several people appear to be gathered around a model of the tower.
Commander Stuart Cundy, from the Metropolitan Police's Grenfell Tower investigation team, said the video would be "fully investigated" to see if any hate crime offences were committed.
'Elhouhabi shamelessly took advantage of the efforts to rehouse people whose homes had been destroyed by claiming his link to one of the flats, and he was subsequently put in hotel accommodation. He said he was "frankly appalled" at the "callous nature" of the clip posted on social media, adding that mocking a disaster like this in such a "crude way" was vile.
"I can't imagine the distress this video will undoubtedly cause to bereaved families and survivors. It can not be justified on any level". "Bye" as she helped lift it into the flames while other people joked about the tragedy that took the lives of 72 people in June past year.
Justice 4 Grenfell, a campaign group honouring the victims, condemned the move as a "sickening act of hate".
Ms Connell added: "My heart really goes out to the Grenfell families - people who have lost loved ones and then have ended up reliving the horror by seeing all this".
On Twitter on Monday evening, London Mayor Sadiq Khan said: "I utterly condemn this sickening video". The residents, many of whom were refugees from Afghanistan, Iraq and North Africa, often complained about being ignored, and the borough council has come under criticism for using cheap cladding on the building, which caused the fire to spread rapidly.