Five men have been arrested in connection with an investigation into a video showing the burning of an effigy of Grenfell Tower.

The Metropolitan police said the men – two aged 49 and the rest aged 19, 46 and 55 – handed themselves in at a south London police station at 10pm on Monday. They were arrested on suspicion of a public order offence and taken into custody.

Police appealed for information after a group of people burned a model of Grenfell Tower and laughed as they pretended to be trapped residents who died in the disaster.

A video posted online showed a large cardboard model marked “Grenfell Tower” being placed over a fire in what appeared to be someone’s back garden, in which an English flag was mounted on a pole.

Bystanders could be heard mockingly saying, “Help me, help me!” and “Jump out the window!” One of them waggled a cutout of a person in a window, several of which appeared to have been coloured brown. To laughter, one person said “Stay in your flat, we are coming to get you”, an apparent reference to the stay-put policy that may have cost lives in the fire on 14 June 2017.

Someone else can be heard saying: “That’s what happens when they don’t pay their rent.”

A still from the video of the mock-up of Grenfell Tower. Photograph: Twitter

It is not known when or where the video was recorded. The participants have southern English accents and one of their faces can be seen reasonably clearly.

Survivors of the blaze described the burning of the cardboard model as a “sickening act of hate” and urged the police to investigate it as a potential hate crime.

A spokesperson for the campaign group Justice4Grenfell said the video had “caused great alarm and distress”, and added: “We are disgusted and shocked at the inhumanity and callousness of those involved in this video.”

Theresa May tweeted: “To disrespect those who lost their lives at Grenfell Tower, as well as their families and loved ones, is utterly unacceptable.”

The government issued a statement condemning the video “in the strongest terms” and urging people not to share it on social media. The 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. Those responsible for this repugnant material are beneath contempt.”

Sajid Javid, the home secretary, called the video “shameful” and Labour’s Diane Abbott described it as “hateful”. Matt Wrack, the general secretary of the Fire Brigades Union, labelled the perpetrators “thick numbskulls”.

Issuing a plea for information, the Scotland Yard commander Stuart Cundy, who is leading the investigation into the Grenfell fire, said he was “appalled by the callous nature of the video posted online” and described it as “vile”.

Natasha Elcock of the community group Grenfell United described the video as “disgusting”. “Not only is it extremely upsetting to survivors and people who lost family, it’s hateful and offensive to everyone that has been affected by the tragic events of that night,” she said.

“We try to keep our focus on the thousands of people across the country who supported us in the weeks after the fire, the hundreds that walk with us every month on the 14th, and everyone who is backing our fight for justice and change.”

Moyra Samuels, part of the Justice For Grenfell campaign group, spoke of the outrage “right across the country, of ordinary decent people who actually saw it for what it was”.

She told BBC Breakfast on Monday it was “a disgusting attack on vulnerable people”, adding: “We have no doubt that there are actually decent, generous people across Britain and this actual act doesn’t represent ordinary British people.

“But there is a worrying rise of racism in this country at the moment. And that is concerning, because it’s now starting to impact on us directly, you know, which means that we actually need to be thinking what we do about this, and how we respond to this as a whole.”