Faouzia and Abdulaziz El-Wahabi, 42 and 52, died alongside their children, Yasin, 20, Huda, 16, and Mehdi, eight, in the flat as the fire ripped through the west London tower block leaving 72 people dead. Now they've been arrested.
The men who are aged between 19 and 55 remain in police custody.
London Police have arrested five men in relation to the video, on suspicion of a public order offence.
The video shows the cardboard model burning on a bonfire, apparently in a private garden, as several adults watch.
The "disgusting and insensitive" video quickly went viral as people watched in shock.
Girl, 10, charged over baby death after 'stamping on head at daycare'
Prosecutors are considering 13 charges against Treu, including four counts of homicide by intoxicated use of a motor vehicle. The hit-and-run suspect later admitted to law enforcement that he had been huffing chemicals before the deadly crash.
Sharife Elouahabi had claimed he lived in the 21st-floor flat where the El-Wahabi family died in the atrocity on June 14, 2017.
"'Bye, everyone!' jeers one member of the group as the design is carried toward a glowing bonfire". Amid the laughter some can be heard saying, "Help me, help me!" and "Jump out the window!" In the background, a St. George's flag can be seen.
Speaking to Tom Swarbrick, Alex described the video as "hilarious".
Prime Minister Theresa May tweeted that the video was "utterly unacceptable", while Home Secretary Sajid Javid dubbed it "disgusting, shameful, behaviour". It also urged anyone present at the gathering to come forward.
Commander Stuart Cundy said: "I am frankly appalled by the callous nature of the video posted online". "When one is ignorant of the world and people that are around them, they do the most stupid and vile things".
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New Zealand were quickly running out of troops - and patience - after a slew of drop ball they simply couldn't find a way through. It didn't really mess with the game much but that's football". "England have been performing like that for quite some time".
"Not only is it extremely upsetting to survivors & people who lost family, it's hateful & offensive to everyone that has been affected by the tragic events of that night", the group said. The Met's Grenfell Tower investigation team is taking this matter very seriously.
The offence can be committed in a public or private place and does not require the person said to have been harassed, alarmed or distressed to be present.
Among the representations on the cardboard tower were women in burqas.
A man has pleaded guilty to fraud after claiming more than £100,000 intended for victims of the Grenfell Tower fire.
Boston Red Sox Tip $195,000 (!!!) on World Series Celebration Drinks Tab
If you start looking at this team, we've got guys from the United States and from the Dominican Republic, Venezuela, Puerto Rico. Red Sox manager Alex Cora greets Puerto Rican governor Ricardo Rosselló upon arriving in Puerto Rico .