Sir Keir Starmer has promised communities they “will be safe” in the face of ongoing disorder in UK towns and cities.

After chairing a second Cobra emergency meeting since the unrest began a week ago, the prime minister said the government was doing “everything we can” to ensure police could respond wherever they were needed.

Nearly 6,000 public order officers are being mobilised to respond to any disorder in the coming days, according to police sources.

More than 400 arrests have been made so far after days of disorder following the killing of three girls in Southport, fuelled by misinformation spread online that the suspect was an asylum seeker.

It is understood there are at least 30 potential gatherings planned for Wednesday that police are aware of but they believe the situation is “manageable”.

Police hope to be “through the worst” of the disorder but are ready to respond if the situation escalates, sources said.

Meanwhile, immigration lawyers have told the BBC they fear being attacked after their workplaces were on a list of offices circulated on social media.

They said they had been advised by police to work from home, board up office windows and install fireproof letterboxes.

After Tuesday evening’s Cobra meeting, attended by ministers and members of law enforcement, Sir Keir repeated his message that those taking part in unrest would “feel the full force of the law”.

About 100 people have now been charged in relation to the disorder, with more suspected rioters appearing in court on Tuesday, and Sir Keir said he expected “substantive sentencing” by the end of this week.

“That should send a very powerful message to anybody involved, either directly or online, that you are likely to be dealt with within a week,” he said.

On Tuesday, James Nelson, 18, was jailed for two months for causing criminal damage during disorder in Bolton, Greater Manchester. He is believed to be the first person to receive a prison sentence for his role in the unrest.

In a message of reassurance to people concerned about the threat of disorder, the PM said: “It’s a difficult situation with disorder going on in a number of different places at the same time, but that is precisely why I held my second Cobra meeting today to co-ordinate the response and to get the assurance that I want and need, that we do have adequate police in place, that we are able to cope with this disorder.”

Home Secretary Yvette Cooper earlier pledged the government would support police with additional costs for officers working overtime.

In addition to more riot police being put on standby, forces are also stepping up neighbourhood policing patrols while teams of detectives investigate.

They are drawing on CCTV, body-worn footage and retrospective facial recognition to identify perpetrators of violence, while intelligence teams monitor well-known influencers and organisers for activity.

Durham Constabulary said officers had issued dispersal orders to 37 people who had gathered in the city centre on Tuesday evening. A 15-year-old was arrested but police said they had received no reports of incidents of disorder or criminal damage.

The Metropolitan Police said it was “aware” of events planned in London on Wednesday and would “use every power, tactic and tool available to prevent further scenes of disorder”.

Police in Bristol said they “do not believe” there will be an anti-immigration march in the city on Wednesday following claims on social media, though additional resources would still be deployed.

The government earlier said it would make more than 500 new prison places available to ensure those taking part in the violence could be jailed.

Justice Minister Heidi Alexander said 567 additional prison places would soon be available, including extra cells at HMP Stocken, Rutland, and places at Cookham Wood Young Offender Institution in Kent for adult prisoners.

Carl Davies, vice-president of the Prison Governors’ Association, told the BBC the extra places were “not an accounting trick”, though the government might face challenges staffing them.

But he warned the justice system was “still reeling from the impact of austerity”, adding that: “To think we can already turn on the system to respond in the same way we did to the 2011 riots is probably a bit unrealistic.”

Following riots in August 2011, 1,984 suspects had faced prosecution by October, with 686 found guilty.

Sir Keir praised the criminal justice system for a “robust and swift response” in the face of ongoing unrest, which he said was “very important to sending a message in circumstances like this”.

Earlier the director of public prosecutions, Stephen Parkinson, told the BBC prosecutors were considering terrorism offences for some suspects.

He also said his teams would consider seeking the extradition of social media influencers allegedly playing a role in the disorder from abroad.

Separately a 28-year-old man was charged with posting content online that was allegedly intended to stir up racial hatred in relation to the violent disorder – the first such charge in relation to the clashes.

More suspects appeared in court on Tuesday:

The BBC followed events in Sheffield Magistrates’ Court as six defendants, including teenagers, appeared in court over their alleged role in the trouble in Rotherham. A 25-year-old became the first person to be convicted in relation to disorder outside a hotel housing asylum seekers after pleading guilty to kicking a police officer.

A 15-year-old boy is due to appear in court on Wednesday following unrest in Belfast in the early hours of Tuesday.

Meanwhile, an assault on a man in his 50s who was left in a serious condition on Monday evening is being investigated as a racially motivated hate crime, police in Belfast said.