Far-right marches took place across the UK on Saturday after violent unrest in Belfast and Southampton in recent days.

Several people were arrested on Saturday afternoon as far-right groups clashed with anti-racist and anti-fascist demonstrators in Brighton, Liverpool, Sheffield and Glasgow.

Homes and vehicles were set on fire in Belfast this week after Stephen Ogilvie, 44, lost an eye after a knife attack in the city on Monday evening. Hadi Alodid, 30, originally from Sudan, has been charged with attempted murder.

This week, five people were also jailed for violent disorder after riots broke out in Southampton in response to the death of Henry Nowak.

Nowak, an 18-year-old student, was arrested in error over false racism claims while dying of stab wounds inflicted by Vickrum Digwa, a British Sikh. The protests took place earlier this month, shortly after Digwa was jailed for Nowak’s murder.

On Saturday, a protest was held in Sheffield by Raise the Colours, which describes itself as a “grassroots movement for unity and patriotism” and campaigns against illegal immigration.

South Yorkshire police said five people were arrested. Four men have been accused of public order offences, while another was arrested on suspicion of assault. A 17-year-old boy was detained after an alleged attack on an emergency worker.

Supt Charlotte Bloxham said the force’s operation was “complicated by a counter-protest group which did not adhere to conditions in place”.

However, she added that officers “were able to safely manage the protest and counter-protest throughout”.

In Brighton the anti-immigration group South East Patriots and counter-protesters from an event called Carnival Against Fascism took to the streets.

South East Patriots said it was calling for stronger border control, enforcement of immigration laws, and the deportation of illegal immigrants.

More than 20 anti-racist groups took part in the counter-demonstration, including the DJ Fatboy Slim. They said they were coming together to “ensure a united resistance” and to show “the far right are not welcome in Brighton”.

Footage of minor skirmishes between the two groups circulated on social media, with tensions concentrated around Brighton railway station.

The far-right demonstrators, many of whom were draped in the flag of St George and the union jack, were contained by the police on Terminus Road, which runs alongside Brighton railway station. Counter-protesters faced off with them through the gates of the station, with both groups trading insults and songs.

A Sussex police spokesperson confirmed that officers had arrested a man on suspicion of breaching the peace and assaulting a police officer. Another man was detained in relation to an alleged public order offence in a separate incident at the same protest, the force said.

In Liverpool, protesters clashed in the Walton area of the city, as rightwing groups led chants calling for mass deportations. Merseyside police said they had arrested a man on suspicion of breach of the peace.

The unrest took place as Andy Burnham said the UK was on a path towards the “poisonous” politics of the US under the current Labour leadership.

During a campaign speech on Saturday, the mayor of Greater Manchester said discourse was becoming more polarised and “communities don’t work together any more”.

Burnham, who hopes to return to Westminster in next week’s Makerfield byelection, asked people attending the speech: “Does anyone here feel that we can just stay on the path that we’re on as a country?

“It doesn’t feel doable, does it? It doesn’t feel that we’re heading in the right direction. It doesn’t feel like we’re heading to better lives for people.

“Things are getting harder, and politics is getting more polarised, and the path we’re on, if we are not careful, is a path towards the politics of the United States of America, a polarised, poisonous politics where people in communities don’t work together any more.”

Also on Saturday, rival protesters clashed in Glasgow after thousands descended on the city for a “reclaim our streets” demonstration organised by Stand Up to Racism.

The anti-racism protesters gathered near a significantly smaller group of counter-protesters who were fenced off from the main group by police.

Some in the counter-protest group performed what appeared to be Nazi salutes as the two groups gathered in the city centre.

Most of the counter-protesters, who were almost exclusively men, wore balaclavas or other face coverings.

The scene became tense as police tried to contain counter-protesters who had attempted to breach the barriers.

Projectiles, including drink cans, were thrown towards the Stand Up to Racism group, while an egg appeared to be thrown towards the counter-protesters.

Some of the counter-protesters waved union flags, and others Israel flags, while the anti-racism side waved Palestinian, Ukraine and Scotland flags.