Six men arrested over a video of a model of Grenfell Tower being burned at a bonfire party have been released under investigation.

The men were held on suspicion of the public order offence of causing another person harassment, alarm or distress.

Five of them handed themselves in on Monday night – a 19-year-old, a 46-year-old, two 49-year-olds and a 55-year-old – while the sixth man, aged 19, was arrested on Tuesday after attending a south London police station.

The video, showing people mocking the plight of Grenfell victims as the cardboard model burned, drew condemnation from survivors of the deadly blaze last year, as well as the prime minister, Theresa May, and the chairman of the public inquiry into the disaster, Sir Martin Moore-Bick.

Plainclothes detectives searched a house in South Norwood in south London on Tuesday as part of their investigation. Three officers were at the property for about two hours and took away two clear plastic bags that appeared to contain gaffer tape and white tags.

After leaving the house, officers searched bins under the front window and knocked on neighbours’ doors.

Survivors of the fire described the incident as a “sickening act of hate” and urged the police to investigate it as a potential hate crime. Lines of inquiry are understood to include whether the bonfire party was open to the public and whether the video was intentionally put online. The men were arrested under section 4a of the 1986 Public Order Act, which deals with threatening, abusive or insulting words or behaviour.

A defence could be that the accused were inside a dwelling and had no reason to believe what they did would be heard or seen by people beyond. The video is believed to have been circulated originally on WhatsApp before being posted to social media, at which point it was reported to the police.

The model of Grenfell Tower included paper figures of people at the windows. 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. Another person said: “That’s what happens when you don’t pay your rent.”

An image from the video, believed to have originally been circulated on WhatsApp. Photograph: Twitter

Sam Davis, a neighbour, said she was appalled by the video. “Having the idea is one thing, then you get the cardboard box, then you go and get the tape. For me, the worst of it all is the cutout people with their hands in the air. That is the most disgusting, horrific, selfish [thing].”

Another neighbour saw the bonfire from his upstairs window. “There was drink, they were moving around the fire and letting the fireworks off,” he said. “The fireworks seemed quite expensive; they were big bangs. It’s not nice, is it? People from all over the world live up this street, they can’t be very pleased about it.”

Dr John Green, who is leading the NHS’s mental health response to the disaster, said: “Our main concern now is that it will cause further anguish to people from Grenfell and to those who lost someone in the fire.” He urged people who were struggling to contact the helpline.

Natasha Elcock, the chairwoman of Grenfell United, said she feared the video reflected “judgment and misperceptions” among some parts of society that the community group had been “fighting since day one”, and cited the view expressed in the clip that the tower’s residents did not pay rent.

“Unfortunately many of those early misperceptions have stuck and without really looking for the truth, some members of the public believe what they read and hear,” Elcock said. “It is a narrative that we are still trying to correct.”

The Royal Borough of Kensington and Chelsea, which owns the block, said only 44 of the 115 rentable tenancies in the tower were covered entirely by housing benefit, and 40 households received no housing benefit at all. Other flats were owned by leaseholders.

The Scotland Yard commander Stuart Cundy, who is leading the investigation into the Grenfell Tower fire, which claimed 72 lives, said he was “appalled by the callous nature of the video posted online”.

In the footage, bystanders could be heard mockingly saying: “Help me, help me!” 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.

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

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