Prime Minister Rishi Sunak used a Friday evening address to warn that democracy is being targeted by extremists.
Mr Sunak said there are “forces here at home trying to tear us apart”.
Speaking at a lectern outside the doors of No 10 Downing Street, Mr Sunak warned about the current situation in Britain, in the aftermath of the October 7 attacks by Hamas against Israel.
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And he said the victory of George Galloway in the Rochdale by-election was “beyond alarming”.
“In recent weeks and months, we have seen a shocking increase in extremist disruption and criminality,” he said in a hastily arranged address to the nation.
“What started as protests on our streets have descended into intimidation, threats and planned acts of violence.
“Jewish children, fearful to wear their school uniform lest it reveals 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. Council meetings and local events have been stormed. MPs do not feel safe in their homes. Long-standing parliamentary conventions have been upended because of safety concerns.
“And it’s beyond alarming that last night, the Rochdale by-election returned a candidate that dismisses the horror of what happened on October 7, who glorifies Hezbollah and is endorsed by Nick Griffin, the racist former leader of the BNP.”
In his victory speech, newly elected Rochdale MP George Galloway announced that his win was “for Gaza” following a feisty campaign dominated by the conflict.
Mr Sunak, in a message aimed at those taking part in pro-Palestine protests, urged people to reject extremist messages.
The Conservative Party leader said: “I want to speak directly to those who choose to continue to protest: don’t let the extremists hijack your marches.
“You have a chance in the coming weeks to show that you can protest decently, peacefully and with empathy for your fellow citizens.
“Let us prove these extremists wrong and show them that even when we disagree, we will never be disunited.”
Further local demos are planned for this weekend before another national march, organised by the Palestine Solidary Campaign, takes place in central London on Saturday March 9.
The Prime Minister said a line has to be drawn so that while people should be able to “march and protest with passion” in support of Gaza, demonstrators “cannot call for violent jihad”, justify the actions of Palestinian militant group Hamas — a proscribed group in the UK, which bans any show of support — or “call for the eradication of a state or any kind of hatred or antisemitism”.
He confirmed he has met senior police chiefs to tell them the public expected the pro-Palestine protests to be policed rather than simply managed.
“I say this to the police, we will back you when you take action,” he said.
He said those instructions to police would be backed up by further action from the Government.
What he called a “new robust framework” would be introduced to “ensure we are dealing with the root cause of this problem”, the Prime Minister said.
Mr Sunak said ministers would redouble their support for the anti-terrorism Prevent programme, demand universities stop extremist activity on campus and act to prevent people from entering the country whose “aim is to undermine its values”.
He also said Home Secretary James Cleverly has instructed that those in the UK on visas who choose to “spew hate” will have their right to be in the country removed.
“You cannot be part of our civil life if your agenda is to tear it down,” he warned.
The Prime Minister spent most of Friday in Scotland, giving a speech to the Scottish Conservative conference in the afternoon.
Shortly after the Conservative leader had finished taking questions from party members in Aberdeen, No 10 confirmed he would be travelling immediately to London.
His decision to focus on division in Britain was condemned by critics who accused the Prime Minister and other senior Tory figures of having helped “sow the seeds of division for years”.
Former deputy Tory chairman Lee Anderson was stripped of the party whip last weekend after he accused Sadiq Khan, the Labour mayor of London, of being controlled by Islamists, and Home Secretary Suella Braverman regularly branded protests in favour of a ceasefire in the Middle East as “hate marches”.
Liberal Democrat leader Sir Ed Davey, who urged Mr Sunak to call a general election, said: “The British people will take no lessons from a Prime Minister and Conservative Party who have sowed the seeds of division for years.
“This is the same Prime Minister who made Suella Braverman his Home Secretary and Lee Anderson his party’s deputy chairman.”
Sir Keir Starmer, the Labour leader, appeared to back Mr Sunak’s intervention.
In a statement, he said: “The Prime Minister is right to advocate unity and to condemn the unacceptable and intimidatory behaviour that we have seen recently.
“Citizens have a right to go about their business without intimidation and elected representatives should be able to do their jobs and cast their votes without fear or favour.”
Organisers of the pro-Palestinian demonstrations this week vowed to continue protesting at least until a ceasefire in the Israel-Hamas war is reached.
They also defended using the “from the river to the sea, Palestine will be free” chant, a slogan some critics claim calls for the eradication of the state of Israel.
Further casualties this week in Gaza, which has come under a constant barrage of Israeli attacks in the past five months, saw the Palestinian death toll pass 30,000, according to the Hamas-run health ministry.