The London residential block went up in flames in June last year, claiming 71 lives. It was Britain's worst residential fire since World War II.
The video clip, posted online, showed a large effigy marked "Grenfell Tower", complete with paper figures at the windows, being set ablaze on a bonfire. Raucous laughter can be heard.
"Five men have been arrested on suspicion of a public order offence in connection with an investigation into a video posted online that showed an effigy of Grenfell Tower being burnt," Scotland Yard police headquarters said in a statement.
The men, aged 19, 46, 49, 49, and 55, were arrested after handing themselves in at a south London police station late Monday.
"They have been taken into custody," police said.
In the video, onlookers can be heard saying: "Help me! Help me!", "Jump out the window!" and "That's what happens when they don't pay their rent." The Grenfell United organisation for survivors and the bereaved, tweeted: "It's a disgusting video.
"Not only is it extremely upsetting to survivors and people who lost family, it's hateful and offensive to everyone that has been affected."
Prime Minister Theresa May tweeted: "To disrespect those who lost their lives at Grenfell Tower, as well as their families and loved ones, is utterly unacceptable." Police Commander Stuart Cundy, who is leading the investigation into the Grenfell disaster, said he was "frankly appalled by the callous nature" of the video.
Bonfires are traditional in Britain around November 5, recalling a foiled plot to blow up parliament in 1605. Effigies of plotter Guy Fawkes are burned on the fire.
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