Two men and a teenage boy have been arrested in Portsmouth at a far-right protest against immigration.

Far-right activists have gathered in Portsmouth for a second weekend after a small boat with 140 people seeking asylum on board was intercepted last Sunday while heading towards the city.

They were greeted by counter-protesters as police warned they would not tolerate incitement of fear or violence.

One of the arrested, a 76-year-old man from Southampton, was detained on suspicion of concealing his identity at the Portsmouth protest. Hampshire and Isle of Wight constabulary had warned that protesters wearing face coverings could be arrested under powers in the Crime and Policing Act.

A 33-year-old man from Portsmouth was also arrested on suspicion of obstructing a highway and a 16-year-old boy, also from Portsmouth, was arrested on suspicion of violent disorder in relation to scenes last Sunday.

Donna Jones, the police and crime commisioner for Hampshire and Isle of Wight, said that they “thankfully didn’t see repeated scenes of Sunday night with assaults on police officers and criminal damage to police vehicles and people’s property” and that “with the exception of a few people, it was peaceful and conducted in accordance with the new law calling for their faces to be uncovered”.

Jones added: “The people of Portsmouth deserve to go about their business without fear and disruption.

“While some may think it was arbitrary to use the new power directing people to remove face coverings, the police ensured it was implemented equally and impartially for everyone involved.

“I will ensure this power is used proportionately in the future for both sides of the spectrum of protesters.”

In Portsmouth city centre, there was a large police presence where demonstrators assembled to march on Saturday.

Some protesters held union flags while some wearing Portsmouth patriot branded clothing gathered outside All Saints Church on Commercial Road.

A man with a megaphone got the crowd chanting “stop the boats”. He said the protest was against “illegal men invading the shores”.

In the neighbouring car park, demonstrators holding Stand Up to Racism (SUTR) and Refugees Welcome banners gathered. Signs included: “RNLI are heroes, no one is illegal” and “stop pretending your racism is patriotism”.

Hundreds of people also gathered in Glasgow for an anti-immigration rally and associated counter-protest.

The Pink Ladies movement organised their event at Glasgow Green, prompting opposing groups, including SUTR, to arrange a counter-protest.

The two groups were contained in separate areas on the eastern side of the park, with the People’s Palace and a heavy police presence between them.

Ch Supt Stevie Dolan warned of a “strong response” if there was any violence after flashpoints at a previous protest in the same park in July.

MSPs Alison Thewliss, a Scottish government minister, and Iris Duane were at the SUTR rally, with the Scottish Trades Union Congress general secretary Roz Foyer.

Prominent figures on the Scottish right, such as Reform UK’s deputy leader in Scotland, Thomas Kerr, and the Reform councillor Audrey Dempsey, attended the Pink Ladies event.

Saturday’s protests came after hundreds of far-right activists descended on Portsmouth last Sunday after a small boat crossing the Channel approached the city. The demonstrators tried to stop those onboard from being processed.

Hampshire police said: “We will support those who want to express their views peacefully and lawfully, but we will not tolerate those whose only aim is to create fear and incite violence.”

The opposing groups were allocated specific locations at which they could gather under protest conditions. Failure to comply with conditions could lead to arrest, police said. The anti-immigration protest marched to Guildhall Square and the counter-protest followed later on the same route.

The incident with the small boat last Sunday is thought to be the first time such a large vessel containing asylum seekers has been brought to Portsmouth and the first time a significant group of anti-migrant protesters have tried to block newly arrived asylum seekers from being processed.

Small boat crossings have fallen by more than 40% compared with the same period last year. While the Home Office has disrupted the smugglers’ business model, their methods appear to have evolved by launching boats – such as the one that arrived on last Sunday – from different parts of the French coast much farther from the UK, making the crossings more dangerous.

Most small boat arrivals are rescued by Border Force and RNLI vessels on the English side of the Channel and brought ashore at Dover. RNLI volunteers and staff have faced abuse from protesters over their rescue work bringing some small boat migrants ashore.

The first man charged over last weekend’s anti-migrant demonstration in Portsmouth appeared in court on Saturday.

Del Leon Somerville, 42, of Paulsgrove in Portsmouth, appeared before the city’s magistrates court charged with violent disorder and assaulting a police constable in the execution of their duty.

Assistant chief constable Tony Rowlinson said Somerville’s arrest was the “first of what we fully anticipate to be a number of arrests” and hoped it would send a “clear warning” to those planning future disruption and disorder.

The government condemned what it described as the “thuggish behaviour” of the protesters last Sunday. “We condemn the intimidating and thuggish behaviour we are seeing tonight,” a government spokesperson said. “The right to peaceful protest is fundamental to our democracy, but it must never cross a line into disorder.”

The home secretary, Shabana Mahmood, met police on Thursday for reassurance they are ready to move quickly in dealing with “far-right groups” seeking to intimidate communities after last weekend’s events in Dover and Portsmouth. Official vehicles were damaged in Portsmouth and a small number of officers were injured, police said. In Dover, crowds of masked men blocked road access to the port in scenes that were condemned by politicians of all parties.

Mahmood said: “These scenes have caused disruption for people and, given that people are dressed in black wearing balaclavas, there is a fear factor and obvious malign intent being communicated to our residents.

“This makes it different from other protests, so we need to make sure we are learning lessons.”