Various male voices are heard making cruel quips about the tragedy, which killed 72 people on June 14 past year after the blaze quickly engulfed the west London block.
Communities Secretary James Brokenshire said: "At a time when the bereaved and survivors are giving testimony to the Grenfell inquiry and reliving the unimaginable horror of that tragedy, it beggars belief that anyone should do this".
And now the identity of the culprits - who set alight a 1m tall cardboard mock-up of the London apartment tower decorated with racist figures-have been revealed.
Commenting on the video, one person said: 'So sad let's all hope one day it's not them'.
A spokesman added: "We are disgusted and shocked at the inhumanity and callousness of those involved in this video".
Another Twitter user responded: "Now I think these people are sick and I think this is absolutely disgusting but a hate crime?" They were all arrested on a public order offence and taken into custody by the Met Police.
"Help me, help me", someone can be heard saying at one point. "Help me, help me", another man shrieks, apparently in jest, as the fire climbs the paper model.
The video ends as the model is completely consumed by the fire, with one bystander saying: "Perfect".
Arsene Wenger 'close to becoming new AC Milan manager'
The father and son billionaires are understood to be Arsenal fans and are keen for Wenger to replace Gattuso at the helm.
"The content of the video, that includes a replica model of Grenfell Tower and the burning of effigies, has caused great alarm and distress".
Speaking to Tom Swarbrick, Alex described the video as "hilarious".
Meanwhile, the Prime Minister, fire chiefs and victims have condemned the partygoers.
Natasha Elcock, from Grenfell United, said: "It's a disgusting video".
Five men have been arrested over a video showing a laughing group of people burning a model of the Grenfell Tower, British police said Tuesday.
In a statement, London's Metropolitan Police Service called the video "vile" and urged people with information to come forward.
Councillor Elizabeth Campbell, leader of Kensington and Chelsea Council, said: "I can not believe somebody would do this, it is absolutely despicable. Families who lost loved ones in the tragedy have been through so much, but have always conducted themselves with such dignity, they should be given much more respect".