GEOFF BENNETT: In Britain, the government there is planning new legislation to punish extremists responsible for rising tensions over the war in Gaza.

As special correspondent Malcolm Brabant tells us, Prime Minister Rishi Sunak is concerned that both Jewish and Muslim communities are being targeted and that social cohesion is under threat.

MALCOLM BRABANT: Support for the Palestinian cause in the city of Brighton is particularly vocal, and protesters wore black to mourn for Gaza and show disdain for Rishi Sunak's urgent speech to the nation last Friday.

RISHI SUNAK, British Prime Minister: In recent weeks and months, we have seen a shocking increase in extremist disruption and criminality.

What started as protests on our streets has descended into intimidation, threats and planned acts of violence.

MALCOLM BRABANT: The Brighton demonstration was peaceful, but organizer Russell Craddock didn't like the scrutiny of our camera.

RUSSELL CRADDOCK, Palestinian Solidarity Campaign: Who are you filming for?

MALCOLM BRABANT: American television.

RUSSELL CRADDOCK: Oh.

I'm not giving you permission to film.

MALCOLM BRABANT: I have permission to film because this is an open space.

RUSSELL CRADDOCK: Does someone want to stand in front of him?

MALCOLM BRABANT: Freedom to film in public places is a longstanding British tradition, but national values, including tolerance, are under strain.

RISHI SUNAK: Jewish children fearful to wear their school uniform, lest it reveal their identity, Muslim women abused in the street for the actions of a terrorist group they have no connection with.

Now our democracy itself is a target.

MALCOLM BRABANT: Across the square, Jewish residents stood guard around a memorial to victims of the Hamas terrorist attack on Southern Israel on October the 7th.

ADAM MA'ANIT, Jewish Community Leader: The day after the October 7 massacres, on October 8, they had a demonstration in the center of the city, and they had a speaker who praised the October 7 massacre and said that it was a day of celebration.

That's who these people are.

MALCOLM BRABANT: Adam Ma'anit's 18-year-old cousin, Maayan, was murdered on October the 7.

Her father was kidnapped and remains a hostage.

ADAM MA'ANIT: You speak to any Jew in the country, many of them will be experiencing heightened sense of insecurity and fear from weekly protests, people shouting at them when they exit their synagogues, people harassing them on social media.

I mean, social media is a sewer right now.

MALCOLM BRABANT: On the other side of town, former dancer Lee Whitaker carried a bundle to represent children killed by Israel's bombardment of Gaza.

LEE WHITAKER, Pro-Palestinian Protester: You can see what extremists we are.

And that is just Rishi Sunak.

He's making trouble.

It's actually our protests are protests of love.

The big thousands of us marching in London, I have never seen any trouble.

There's such a wonderful feeling of camaraderie.

MALCOLM BRABANT: In London, the mayor, Sadiq Khan, is concerned that anti-Muslim bigotry is also on the rise.

SADIQ KHAN, Mayor of London: What we're witnessing is a concerted and growing attempt by some to degrade and humiliate minorities for political and electoral gain.

MALCOLM BRABANT: But an angry and chaotic debate in Parliament about Gaza last month raised fears about intimidation.

House Speaker Lindsay Hoyle: SIR LINDSAY HOYLE, Parliament Speaker, United Kingdom: I am very, very concerned about the security of all members.

PROTESTER: From the river to the sea!

PROTESTER: Palestine will be free!

MALCOLM BRABANT: This chant is at the center of government concerns.

While some right-wing Israeli factions use "From the river to the sea" to taunt Palestinians about expulsion, Jewish groups regard the pro-Palestinian version as a threat to wipe Israel off the map.

It was projected onto Parliament's clock tower as members were arguing about the war.

RISHI SUNAK: M.P.s do not feel safe in their homes.

There is no context in which it can be acceptable to beam antisemitic tropes onto Big Ben in the middle of a vote on Israel-Gaza.

JONATHAN HALL K.C., Independent Reviewer of Terrorism Legislation: No, I don't think it was just politicking.

He was effectively drawing attention to what he and I think also the official opposition regard as something of real significance, and if not urgency.

MALCOLM BRABANT: Jonathan Hall monitors extremism as part of his role reviewing Britain's terrorism laws.

JONATHAN HALL K.C.

: I haven't seen such open hostility towards categories of individuals as I have since the 7th of October.

That willingness, almost a brazenness to go out on the streets and to be really vile and horrible and invite hatred and in some circumstances violence against people by category is something that we haven't really seen.

MALCOLM BRABANT: In Brighton, demonstration organizer Russell Craddock gave his verdict on Rishi Sunak's plans to crack down on extremism.

RUSSELL CRADDOCK: We won't be intimidated by Sunak.

We won't be intimidated by the Met.

We won't be intimidated by so-called claims of violent antisemitism.

MALCOLM BRABANT: But this was Russell Craddock the day after the Hamas terrorist attack.

RUSSELL CRADDOCK: So, amazingly, incredibly, most of the Hamas fighters paraglided their way.

(CHEERING) JONATHAN HALL K.C.

: Someone who glorifies a terrorist organization and is reckless, so takes the risk that someone will be encouraged to support that organization, does commit an offense.

MALCOLM BRABANT: The Kaddish, traditional Jewish prayer of mourning, next to a memorial that has frequently been vandalized.

Across town, white flags for the Palestinian dead, and that chant, which local police say can warrant arrest in aggravating circumstances.

PROTESTER: From the river to the sea!

PROTESTERS: Palestine will be free!

MALCOLM BRABANT: We approached the man with the megaphone.

From American TV.

Can I ask you a question please?

PROTESTER: Go ahead.

MALCOLM BRABANT: Can you just explain to me... (CROSSTALK) PROTESTER: Don't -- don't.. MALCOLM BRABANT: No, I'm allowed to do this because this is a public... PROTESTER: No, you're not allowed to take photo of me.

MALCOLM BRABANT: Yes, I am.

I'm -- it's a public space.

PROTESTER: We're here to support people that have been massacred and murdered, children and babies, and you're here sticking (INAUDIBLE) in people's faces.

MALCOLM BRABANT: No.

PROTESTER: Don't you think that's disgraceful?

MALCOLM BRABANT: No, I don't.

I'm just merely asking a question.

(CROSSTALK) PROTESTER: No, you're not.

MALCOLM BRABANT: Yes, I am.

PROTESTER: You came and picked on this man.

MALCOLM BRABANT: Because he was actually chanting.

PROTESTERS: Palestine!

Free, free, Palestine!

PROTESTER: From the river to the sea!

MALCOLM BRABANT: The police ushered us away because, here, asking questions risks a breach of the peace.

For the "PBS NewsHour," I'm Malcolm Brabant.