Theresa May insisted that Britain's democratic process would not be "deterred"
Asked at an election rally in Stoke on Trent if voters should be worried about the possibility of further attacks on polling day, she said: "The national threat level is at severe, which does mean that a terrorist attack is highly likely.
"It has been severe for some time. People have been planning, ensuring people's safety on that basis.
People should go out there to vote – I want to see people going out to vote because I think that is a very important message, that our democracy will not be deterred
"People should go out there to vote – I want to see people going out to vote because I think that is a very important message, that our democracy will not be deterred."
Mrs May brushed aside claims about intelligence failings by the security services in the run up to the latest attacks.
"We need to ensure that MI5 and the police are able to get on with that investigation as they need to do now.
Mrs May brushed aside claims about intelligence failings
"Then we will look at how the processes were followed, what they did.
"They will want to be looking at that because they will want to learn lessons for the future, if there are those lessons to be learned," she said.
She added: "The police and Security Service have done a good job in foiling a number of plots – just five in the last three months, and a significant number in the last few years as well.
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Mrs May said the national threat level remains at severe
"Vowing to crack down on terrorist on the internet, she said: "I think the companies should accept their responsibility in relation to what is being put on their platforms, because frankly we see hateful ideology being spewed across their platforms by the extremists.
"That can lead to terrorism, and we don't want to see a safe space online for terorrists to plane their attacks. Se we will continue to put pressure with others on those companies.
"But we're also very clear we do need to look at regulation for cyber space because we need to ensure there is no safe space for terrorists online."
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The Prime Minister said we need to look at regulation for cyber space
In an interview with Sky News, the Prime Minister added: "MI5 and the police have already said they would be reviewing how they dealt with Manchester and I would expect them to do exactly the same in relation to London Bridge.
"What government needs to do is, and what the government that comes in after Thursday's election needs to be willing to do, is to give more powers to the police and security service when they need them, needs to deal with this issue of terrorism and extremism online and also needs to be able to call out extremism here in the United Kingdom."