May said on Sunday that a new approach to tackling extremism is required, including changes that would deny terrorists and extremist sympathizers digital tools used to communicate and plan attacks.
May said: "We can not allow this ideology the safe space it needs to breed".
May responded to the attack by calling for an overhaul of the strategy used to combat extremism, including a demand for greater global regulation of the internet, saying big internet companies were partly responsible for providing extreme ideology the space to develop. We now need to see the same response in terms of extremism and radicalisation.
Not everyone is convinced that additional restrictions would be effective.
Meanwhile, Professor Peter Neumann, director of the International Centre For The Study Of Radicalisation at King's College London, slammed May's comments as uninformed: "Big social media platforms have cracked down on jihadist accounts, with result that most jihadists are now using end-to-end encrypted messenger platforms e.g".
"Few people (are) radicalised exclusively online", he wrote on Twitter.
The Open Rights Group said it was short-sighted to focus on the Internet and social media networks as the "cause" of problems, and that doing so through narrow-minded regulation would only push militants' communications into the "darker corners of the web".
"This has not solved problem, just made it different", he said on Twitter.
Tech companies have been criticized on disrupting the online terror planning since the most recent attack in London but one cybersecurity analyst told CNBC there is little they can do.
Europe's top regulator released data last week that showed that Twitter has failed to take down a majority of hate speech posts after they had been flagged.
"Terrorist content has no place on Twitter", Nick Pickles, United Kingdom head of public policy at Twitter, said in a statement, adding that in the second half of 2016 it had suspended almost 400,000 accounts. Pickles said the company will "never stop working" on the issue.
Twitter also said it was working to tackle the spread of militant propaganda on its website.
The defences came after May called on social media companies to improve their policies. Police officers pursued and shot dead three attackers within eight minutes of the first emergency call, London police said.