Yvette Cooper has condemned Reform UK for criticising the policing of protests outside a hotel for asylum seekers.

The home secretary said officers deserved public support instead because they kept the country safe.

Nigel Farage, the leader of Reform, called for Ben-Julian Harrington, the chief constable of Essex, to resign after his force escorted anti-fascist protesters through a crowd of people demonstrating against migrants.

But Cooper said: “The police do a really important job across our country keeping people safe. It is really important frankly that people support our police rather than just attacking them continually.

“As we have seen, Reform is one day calling for chief constables to resign, the next it is attacking women police officers who are out on our streets every single day of the week.”

Farage has repeatedly weighed into the debate about the Epping migrant hotel and said this week: “Hard-left groups, Stand Up to Racism and Antifa, were given the red carpet treatment by Essex police, with the force literally escorting and bussing masked thugs to and from the protest. They have been caught red-handed helping to light the fuse that led to violence.”

Harrington said Reform’s claims were “categorically wrong” and that officers had organised a cordon around activists exercising their right to protest.

Dal Babu, a former chief superintendent for the Metropolitan police, said Farage’s claims were wrong and he should correct the public record amid rising tensions.

“British values mean if a politician makes a mistake, they put their hand up and acknowledge it. He knows it is false,” Babu said.

On Thursday, Epping Forest district council unanimously voted to support a motion calling for the immediate closure of the Bell hotel for the purpose of asylum processing and for the “managed closure” of the Phoenix hotel. The vote was non-binding and purely symbolic.

During the meeting Chris Whitbread, the leader of the council, reiterated that the local authority had no say on the use of the hotels and the decision was up to the Home Office, who he accused of “not being overly cooperative” when safeguarding concerns were raised.

Hundreds of protesters, including many women and children, began marching from Epping town centre to the hotel at about 6pm in heavy rain. A ramped-up police operation included fences and a ban on the wearing of facial coverings.

An 18-year-old man was arrested for breaching a section 60AA order, which prevents anyone wearing a face covering.

Police have arrested 17 people in total over protests in Epping.

Activists from the far-right Homeland group were behind an Epping Says No! Facebook group that has been behind much of the promotion of the protests. Members of Patriotic Alternative and White Vanguard have also been involved.

While politicians have largely stayed away from the protest, two Reform councillors were present outside the Epping hotel last week, including James Regan who claimed in an interview that “they’re trying to dilute the Englishness out of us”.

The Guardian also found evidence that a Reform official shared a platform in Epping with an agitator from Homeland.

In last year’s summer riots, Keir Starmer, the prime minister, called out “far-right thuggery” and pledged to bring those involved to justice.

However, the business secretary, Jonathan Reynolds, said on Thursday that many of the Epping protesters were “upset for legitimate reasons”.

Angela Rayner, the deputy prime minister, told the cabinet earlier this week that immigration and deprivation were among the main factors causing public disenchantment with politicians.

There is already a taskforce on community cohesion, informed by experts and officials, while a £1.5bn “plan for neighbourhoods” aims to invest in 75 deprived areas over the next decade.

Some Labour MPs are concerned that political and media language about the UK being on the brink of social unrest may be raising tensions rather than encouraging cohesion.

Stella Creasy, the Labour MP for Walthamstow, said on Thursday that if people were “unsettled by the political and press debate around immigration, law and order, the idea that there could be race riots again, you are completely right to be concerned because this discussion in itself is raising fear and uncertainty and tension”.

She added: “It is dividing us and feeding this myth that Britain is a nation that cannot manage diversity rather than one that draws strength from it.”

Brendan Cox, whose wife, Jo, a Labour MP, was murdered by a far-right extremist, said the UK needed a longer-term strategy on social cohesion.

“There is a set of local concerns around this in Epping and it’s also true that these are being co-opted and used by elements of the far right,” said Cox, who is the convener of an independent commission on community.

“It’s no surprise that happens when there are these kind of festering legitimate concerns and successive governments are seen to not act on those.

“But the broad point I’d make is that we’ve published a report about there being a tinderbox … and I think what’s really clear is that we don’t really have any long-term cohesion strategy at all.”

Nick Lowles, of the Hope not Hate campaign group, said: “We are concerned that policing has not caught up with the new post-organisation nature of the far right, where individuals can emerge and play a role on social media and inciting or directing violence, without ever being a member of a far-right organisation.”

David Blunkett, the Labour peer and former home secretary, said that policing unrest fuelled by the far right was always difficult but the key was “specialist dog-trained police units and an online understanding of what they are doing” – as well as the Home Office involving MI5 at an early stage.

The Epping protest was sparked by the charging of Hadush Gerberslasie Kebatu, a 38-year-old asylum seeker, with sexual assault over allegedly trying to kiss a girl of 14. He denied the charge at Chelmsford magistrates court and will stand trial next month.

A Reform official would not answer questions about sharing a platform with the far right or about Cooper’s claims that the party should back the police.

Instead the spokesperson said the Guardian “cares more about attacking Reform UK than defending young girls who are being abused by illegal boat migrants”.