A similar flag was visible behind the Grenfell model in the video.
Earlier, Scotland Yard has confirmed that five men presented themselves to a police station after an investigation into the video has been launched.
The men, two aged 49 and the others 55, 46 and 19, have been taken into custody by police.
The video is believed to have been circulated originally in closed WhatsApp groups before being posted to social media and shared widely on Twitter and Facebook, at which point it was reported to the police.
Prime Minister Theresa May called the video "utterly unacceptable", and judge Martin Moore-Bick, who is leading an inquiry into the blaze, said it was "shocking and distressing to all those involved". "When one is ignorant of the world and people that are around them, they do the most stupid and vile things. It's like killing these poor people all over again". The video showed one person saying: "That little ninja's getting it at the minute" - an apparent racist comment about a Muslim woman in a burqa depicted on the side of the model.
In the clip posted online, raucous laughter can be heard off camera as the effigy is set alight.
"I can't imagine the distress this video will undoubtedly cause to bereaved families and survivors". "Help me!", "Jump out the window!" and "That's what happens when they don't pay their rent".
The video ends as the model is completely consumed by the fire, with one bystander saying: "Perfect".
The video has been particularly disturbing for many people because the Grenfell tragedy has raised hard issues about race and class in Britain.
Campaigners have described the video as a "sickening act of hate". We hope that the police are taking this seriously.
Natasha Elcock, from Grenfell United, said: "It's a disgusting video". By Monday evening, the video was trending in Britain, with thousands expressing shock and disbelief at the insensitivity of the group in the recording.
"This is clearly a hate crime and as a society we should never tolerate these types of blatant acts of hatred" it said in a statement.
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