The Prime Minister said introducing new rules for cyberspace would "deprive the extremists of their safe spaces online" and that technology firms were not currently doing enough.
She said a new approach to tackle extremism is required, including changes that would deny terrorists and extremist sympathisers digital tools used to communicate and plan attacks.
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Three knife-wielding attackers in fake suicide vests unleashed a terror rampage in the British capital last night, plowing a van into pedestrians on the iconic London Bridge before stabbing revellers in a nearby Borough market.
"We cannot allow this ideology the safe space it needs to breed," May 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 extremist and terrorism planning. And we need to do everything we can at home to reduce the risks of extremism online," she said.
The prime minister said the UK "cannot and must not pretend that things can continue as they are" as she set out tough measures to tackle terrorism in response to the attack.
She said there must be greater regulation of the internet and that existing online "safe spaces" that allow terrorism to "breed" must be eradicated.
The prime minister also said that the government would review its existing counter-terrorism strategy and look at increasing sentences for terror offences.
Iain Duncan Smith, the former work and pensions secretary, backed the Prime Minister and suggested that online companies had "avoided" such a clampdown for "too long".
Duncan Smith described the perpetrators of the London Bridge attack as "scum" and said internet companies must do more to limit the spread of extremist material.
He also suggested that the government should consider introducing "in-house incarceration" for terror suspects.
"To make sure the cyber companies no longer allow our children to be able to go through these sites - lots of parents don't know what their children are looking at right now and only the cyber companies, only these big companies that operate on the internet they need to face up to their responsibilities as well," he said.
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