THERESA May has demanded a global effort to regulate the internet and deny Islamist extremists a “safe space” after the UK’s third deadly terror attack since March.

Warning of a spate of crude but devastating copycat attacks, the Prime Minister also said a blind-eye was turned to extremism in too much of the country, declaring: “Enough is enough."

Speaking in Downing Street after meeting security chiefs, she called for a renewed drive to stamp out extremism across society and an end to “separated, segregated communities”.

She said big internet companies, such as Google and Facebook, must work with governments to stop online extremism, and suggested longer jail terms for terrorism-related offences.

Social media companies have been repeatedly accused of failing to remove extremist content, including recruiting propaganda, bomb and terror attack manuals, and death videos.

Mrs May said: “Everybody needs to go about their lives as they normally would. Our society should continue to function in accordance with our values. But when it comes to taking on extremism and terrorism, things need to change."

Seven people were killed and 48 injured after three men drove a van into pedestrians on London Bridge then rampaged through bars and restaurants with foot-long knives on Saturday night.

HeraldScotland:

Thirty-six people remain in hospital, 21 in a critical condition.

As police and security services began their investigation, 12 people were arrested in Barking, East London yesterday after armed police raided a flat belonging to one of the attackers.

Wearing fake suicide belts to deter bystanders tackling them, the trio slashed and stabbed at the crowds in Borough Market, where witnesses said they shouted, “This is for Allah”.

There were reports of people making frantic efforts to fend them off with bottles and chairs.

A Romanian chef at a bakery in the market was hailed as a hero after hitting an attacker on the head with a crate and sheltering 20 people in his shop by bringing down the shutters.

Gerard Vowls, 47, who had been watching football in the Ship pub, said he saw a woman being stabbed by three men, adding: “They were stabbing everyone. Evil, evil people.”

Another witness told the BBC he had been standing outside Borough tube station when he saw a man with a long knife “stabbing a man, maybe three times, fairly calmly”.

Victims and relatives also spoke of their horror in the aftermath of the carnage.

Australian waitress Candice Hedge, 31, who woke from a coma after being grabbed from behind and stabbed in the throat, said she was in a “bit of pain but would survive”.

Her mother, Kimmi Del Toro, said: “It breaks my heart how terrorists do this. Why? Murderers is what they are.”

Elizabeth O’Neill, whose 23-year-old son Daniel was stabbed in the chest outside a pub, said: “A man ran up to him and said, ‘This is for my family, this is for Islam’ and put a knife in him. “These people say they are doing this in the name of God which is an absolute joke. The first commandment is thou shalt not kill. It is absolutely barbaric and they are absolute cowards.”

Police shot dead all three attackers within eight minutes of the first emergency call at 10.08pm.

The UK’s head of counter-terrorism, Assistant Commissioner Mark Rowley, said eight officers had fired an “unprecedented” 50 rounds in what was clearly a “life and death” situation.

A member of the public suffered a gunshot wound to the head, but is recovering, as are two off duty police officers who were among the injured.

A Canadian and a French citizen were among the dead.

Nicola Sturgeon backed Mrs May’s broad aim but warned civil liberties must not be eroded.

“We must not allow our freedoms and our civil liberties to be undermined. That’s what the terrorists want, and we must come together in a resolution not to allow that to happen.

“These are going to be important debates in the weeks and months to come, and we must have those debates, and we must have them particularly in the few days that lie ahead.”

Google said it was already working with governments “to tackle these challenging and complex problems” and wanted to ensure that “terrorists do not have a voice online”.

Facebook said it wanted to be a “hostile environment for terrorists”, and would “aggressively remove terrorist content from our platform as soon as we become aware of it”.

However the Open Rights Group, which campaigns for internet freedom, said Mrs May “could push these vile networks into even darker corners of the web”, making them harder to track.

Labour's John Mann said internet companies should be made liable for all content they host.

Despite the suspension of election campaigning for most of yesterday, Labour leader Jeremy Corbyn last night accused Mrs May of endangering the public through police cuts.

He said as Prime Minister he would grant the police “full authority to use whatever force is necessary to protect and save life”, but added: “You cannot protect the public on the cheap. The police and security services must get the resources they need, not 20,000 police cuts.

Theresa May was warned by the Police Federation but she accused them of ‘crying wolf’.

“We will recruit another 10,000 new police officers, including more armed police, as well as 1,000 more security services staff to support our communities and help keep us safe.”

Tory security minister Ben Wallace said it was a “desperate” attempt by Mr Corbyn to run from his own record on opposing counter-terror laws and his close relationship with the IRA.

Political leaders from the around the world sent messages of condolence and support, but a row erupted after President Trump criticised the Mayor of London.

Sadiq Khan said the attack had been “cowardly” and “barbaric”, but people should not be alarmed by the presence of more armed and uniformed officers on London’s streets.

In a series of crass tweets, Mr Trump said it was time to “stop being politically correct”, adding: "At least seven dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'" He also said: “Do you notice we are not having a gun debate right now? That’s because they used knives and a truck!”

A spokesman for Mr Khan, Europe’s first Muslim mayor, said Mr Trump was “ill-informed”.

Mrs May, who was Home Secretary for six years before entering Number 10, said the UK was experiencing a new kind of threat “as terrorism breeds terrorism, and perpetrators are inspired to attack not only on the basis of carefully-constructed plots after years of planning and training... but by copying one another and often using the crudest of means of attack.

“We cannot and must not pretend things can continue as they are.”

Taking a far stronger line than in the wake of last month’s Manchester Arena suicide bombing, when she did not mention Islamist extremism, she said change was required in four key areas.

She said the March attack on Westminster Bridge and the Manchester bomb were “not connected by common networks” but bound together “by the single, evil ideology of Islamist extremism. It is an ideology that is a perversion of Islam and a perversion of the truth.”

It would not be defeated by military means alone, but by convincing people British values were “superior to anything offered by the preachers and supporters of hate”.

It must not have “the safe space it needs to breed”, she said, “yet that is precisely what the internet - and the big companies that provide internet-based services - provide.

“We need to work with allied, democratic governments to reach international agreements that regulate cyberspace to prevent the spread of extremism and terrorist planning.”

She went on: “While we have made significant progress in recent years, there is - to be frank - far too much tolerance of extremism in our country.

“We need to become far more robust in identifying it and stamping it out across the public sector and across society.

“That will require some difficult, and often embarrassing, conversations. But the whole of our country needs to come together to take on this extremism, and we need to live our lives not in a series of separated, segregated communities, but as one truly United Kingdom."

The UK’s counter-terrorism strategy also had to be reviewed in response to a “more complex, more fragmented, more hidden" threat.

Indicating the Tories would bring in tougher anti-terror legislation after the election, she said: “We need to make sure the police and security services have all the powers they need.

“And if we need to increase the length of custodial sentences for terrorism-related offences, even apparently less serious offences, that is what we will do.”

One option could be the return of the Blair-era control orders which saw terror suspects relocated, kept under curfew 16 hours a day and denied phone and internet access.

They were replaced by less restrictive “Tpim” orders and electronic tagging in 2011.

Hashid Rashid, secretary general of the Muslim Council of Britain, backed Mrs May and said British Muslims “must play our part" in turning people away from a “death cult”.

He said: "We agree with the Prime Minister that things must change. Enough is enough.

"We are ready to have those difficult conversations, as equal citizens with an equal stake in this fight. I am pleased that the Prime Minister is speaking about conversation, it implies that we must listen to one another and work together to be part of a truly United Kingdom."

He said the Council would work with mosques to report suspicious activity to ensure families were not apart by being victims of terrorism or finding out they had known the perpetrators.

Tory peer baroness Warsi said the attack, during the Islamic holy month of Ramadan, had been committed by “poisonous individuals who are trying to divide our nations”.

All the parties except Ukip suspended election campaigning as a mark of respect for the victims yesterday, but it will resume in full today, with Mrs May expected to visit Scotland.

The national security level, which was raised to critical after Manchester, remains set at severe, indicating the security services do not consider another attack to be imminent.

A benefit concert for the victims of the Manchester bombing took place at Old Trafford amid heightened security last night, with Ariana Grande the main attraction.

The Disney star, whose concert had just ended when 22 people were killed last month, said she was “praying for London” ahead of the event.

Isis were last night celebrated the attack, which represents another shift in terror tactics.

The March attack on Westminster which killed four and injured 50 was carried out by one man using a vehicle and knife; a suicide bomber killed 22 and injured 116 in Manchester; and now three people have used a van and knives to kill seven and injured 48.

Counter-terror agencies have around 500 active investigations involving 3000 persons of interest at any one time, and police have reportedly foiled five terror plots since Westminster.

There will be a minute’s silence in London at 11am on Tuesday.